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c",[583,1081,1083,1145],{"className":1082,"ariaHidden":617},[616],[583,1084,1086,1089,1136,1139,1142],{"className":1085},[621],[583,1087],{"className":1088,"style":626},[625],[583,1090,1092],{"className":1091},[630,631],[583,1093,1095,1128],{"className":1094},[635,636],[583,1096,1098,1125],{"className":1097},[640],[583,1099,1101,1113],{"className":1100,"style":645},[644],[583,1102,1104,1107],{"className":1103,"style":650},[649],[583,1105],{"className":1106,"style":655},[654],[583,1108,1110],{"className":1109,"style":659},[630],[583,1111,607],{"className":1112},[630,663],[583,1114,1115,1118],{"style":666},[583,1116],{"className":1117,"style":655},[654],[583,1119,1121],{"className":1120,"style":674},[673],[676,1122,1123],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,1124],{"d":686},[583,1126,691],{"className":1127},[690],[583,1129,1131],{"className":1130},[640],[583,1132,1134],{"className":1133,"style":698},[644],[583,1135],{},[583,1137],{"className":1138,"style":869},[868],[583,1140,1074],{"className":1141},[873],[583,1143],{"className":1144,"style":869},[868],[583,1146,1148,1151],{"className":1147},[621],[583,1149],{"className":1150,"style":1051},[625],[583,1152,976],{"className":1153},[630,663],". Nach der ",[568,1156,1157],{},"dritten binomischen Formel"," wird der Nenner zu ",[583,1160,1162,1187],{"className":1161},[586],[583,1163,1165],{"className":1164},[590],[592,1166,1167],{"xmlns":594},[596,1168,1169,1184],{},[599,1170,1171,1173,1175],{},[605,1172,607],{},[794,1174,1074],{},[1176,1177,1178,1180],"msup",{},[605,1179,976],{},[1181,1182,1183],"mn",{},"2",[609,1185,1186],{"encoding":611},"b - c^2",[583,1188,1190,1209],{"className":1189,"ariaHidden":617},[616],[583,1191,1193,1197,1200,1203,1206],{"className":1192},[621],[583,1194],{"className":1195,"style":1196},[625],"height:0.7778em;vertical-align:-0.0833em;",[583,1198,607],{"className":1199},[630,663],[583,1201],{"className":1202,"style":869},[868],[583,1204,1074],{"className":1205},[873],[583,1207],{"className":1208,"style":869},[868],[583,1210,1212,1216],{"className":1211},[621],[583,1213],{"className":1214,"style":1215},[625],"height:0.8141em;",[583,1217,1219,1222],{"className":1218},[630],[583,1220,976],{"className":1221},[630,663],[583,1223,1226],{"className":1224},[1225],"msupsub",[583,1227,1229],{"className":1228},[635],[583,1230,1232],{"className":1231},[640],[583,1233,1235],{"className":1234,"style":1215},[644],[583,1236,1238,1242],{"style":1237},"top:-3.063em;margin-right:0.05em;",[583,1239],{"className":1240,"style":1241},[654],"height:2.7em;",[583,1243,1249],{"className":1244},[1245,1246,1247,1248],"sizing","reset-size6","size3","mtight",[583,1250,1183],{"className":1251},[630,1248],".",[564,1254,1255,1256,1406,1407,1550,1551,1252],{},"Das gilt auch für zwei Wurzeln im Nenner: ",[583,1257,1259,1283],{"className":1258},[586],[583,1260,1262],{"className":1261},[590],[592,1263,1264],{"xmlns":594},[596,1265,1266,1280],{},[599,1267,1268,1273,1275],{},[602,1269,1270],{},[605,1271,1272],{},"u",[794,1274,1074],{},[602,1276,1277],{},[605,1278,1279],{},"v",[609,1281,1282],{"encoding":611},"\\sqrt{u} - \\sqrt{v}",[583,1284,1286,1352],{"className":1285,"ariaHidden":617},[616],[583,1287,1289,1293,1343,1346,1349],{"className":1288},[621],[583,1290],{"className":1291,"style":1292},[625],"height:1.04em;vertical-align:-0.2397em;",[583,1294,1296],{"className":1295},[630,631],[583,1297,1299,1334],{"className":1298},[635,636],[583,1300,1302,1331],{"className":1301},[640],[583,1303,1306,1318],{"className":1304,"style":1305},[644],"height:0.8003em;",[583,1307,1309,1312],{"className":1308,"style":650},[649],[583,1310],{"className":1311,"style":655},[654],[583,1313,1315],{"className":1314,"style":659},[630],[583,1316,1272],{"className":1317},[630,663],[583,1319,1321,1324],{"style":1320},"top:-2.7603em;",[583,1322],{"className":1323,"style":655},[654],[583,1325,1327],{"className":1326,"style":674},[673],[676,1328,1329],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,1330],{"d":686},[583,1332,691],{"className":1333},[690],[583,1335,1337],{"className":1336},[640],[583,1338,1341],{"className":1339,"style":1340},[644],"height:0.2397em;",[583,1342],{},[583,1344],{"className":1345,"style":869},[868],[583,1347,1074],{"className":1348},[873],[583,1350],{"className":1351,"style":869},[868],[583,1353,1355,1358],{"className":1354},[621],[583,1356],{"className":1357,"style":1292},[625],[583,1359,1361],{"className":1360},[630,631],[583,1362,1364,1398],{"className":1363},[635,636],[583,1365,1367,1395],{"className":1366},[640],[583,1368,1370,1383],{"className":1369,"style":1305},[644],[583,1371,1373,1376],{"className":1372,"style":650},[649],[583,1374],{"className":1375,"style":655},[654],[583,1377,1379],{"className":1378,"style":659},[630],[583,1380,1279],{"className":1381,"style":1382},[630,663],"margin-right:0.0359em;",[583,1384,1385,1388],{"style":1320},[583,1386],{"className":1387,"style":655},[654],[583,1389,1391],{"className":1390,"style":674},[673],[676,1392,1393],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,1394],{"d":686},[583,1396,691],{"className":1397},[690],[583,1399,1401],{"className":1400},[640],[583,1402,1404],{"className":1403,"style":1340},[644],[583,1405],{}," erweitert man mit ",[583,1408,1410,1432],{"className":1409},[586],[583,1411,1413],{"className":1412},[590],[592,1414,1415],{"xmlns":594},[596,1416,1417,1429],{},[599,1418,1419,1423,1425],{},[602,1420,1421],{},[605,1422,1272],{},[794,1424,973],{},[602,1426,1427],{},[605,1428,1279],{},[609,1430,1431],{"encoding":611},"\\sqrt{u} + \\sqrt{v}",[583,1433,1435,1497],{"className":1434,"ariaHidden":617},[616],[583,1436,1438,1441,1488,1491,1494],{"className":1437},[621],[583,1439],{"className":1440,"style":1292},[625],[583,1442,1444],{"className":1443},[630,631],[583,1445,1447,1480],{"className":1446},[635,636],[583,1448,1450,1477],{"className":1449},[640],[583,1451,1453,1465],{"className":1452,"style":1305},[644],[583,1454,1456,1459],{"className":1455,"style":650},[649],[583,1457],{"className":1458,"style":655},[654],[583,1460,1462],{"className":1461,"style":659},[630],[583,1463,1272],{"className":1464},[630,663],[583,1466,1467,1470],{"style":1320},[583,1468],{"className":1469,"style":655},[654],[583,1471,1473],{"className":1472,"style":674},[673],[676,1474,1475],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,1476],{"d":686},[583,1478,691],{"className":1479},[690],[583,1481,1483],{"className":1482},[640],[583,1484,1486],{"className":1485,"style":1340},[644],[583,1487],{},[583,1489],{"className":1490,"style":869},[868],[583,1492,973],{"className":1493},[873],[583,1495],{"className":1496,"style":869},[868],[583,1498,1500,1503],{"className":1499},[621],[583,1501],{"className":1502,"style":1292},[625],[583,1504,1506],{"className":1505},[630,631],[583,1507,1509,1542],{"className":1508},[635,636],[583,1510,1512,1539],{"className":1511},[640],[583,1513,1515,1527],{"className":1514,"style":1305},[644],[583,1516,1518,1521],{"className":1517,"style":650},[649],[583,1519],{"className":1520,"style":655},[654],[583,1522,1524],{"className":1523,"style":659},[630],[583,1525,1279],{"className":1526,"style":1382},[630,663],[583,1528,1529,1532],{"style":1320},[583,1530],{"className":1531,"style":655},[654],[583,1533,1535],{"className":1534,"style":674},[673],[676,1536,1537],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,1538],{"d":686},[583,1540,691],{"className":1541},[690],[583,1543,1545],{"className":1544},[640],[583,1546,1548],{"className":1547,"style":1340},[644],[583,1549],{}," und erhält ",[583,1552,1554,1572],{"className":1553},[586],[583,1555,1557],{"className":1556},[590],[592,1558,1559],{"xmlns":594},[596,1560,1561,1569],{},[599,1562,1563,1565,1567],{},[605,1564,1272],{},[794,1566,1074],{},[605,1568,1279],{},[609,1570,1571],{"encoding":611},"u - v",[583,1573,1575,1594],{"className":1574,"ariaHidden":617},[616],[583,1576,1578,1582,1585,1588,1591],{"className":1577},[621],[583,1579],{"className":1580,"style":1581},[625],"height:0.6667em;vertical-align:-0.0833em;",[583,1583,1272],{"className":1584},[630,663],[583,1586],{"className":1587,"style":869},[868],[583,1589,1074],{"className":1590},[873],[583,1592],{"className":1593,"style":869},[868],[583,1595,1597,1600],{"className":1596},[621],[583,1598],{"className":1599,"style":1051},[625],[583,1601,1279],{"className":1602,"style":1382},[630,663],[559,1604,1606],{"id":1605},"beispiele","Beispiele",[583,1608,1611],{"className":1609},[1610],"katex-display",[583,1612,1614,1684],{"className":1613},[586],[583,1615,1617],{"className":1616},[590],[592,1618,1620],{"xmlns":594,"display":1619},"block",[596,1621,1622,1681],{},[599,1623,1624,1635,1637,1659,1661,1673,1675,1677],{},[1625,1626,1627,1630],"mfrac",{},[1181,1628,1629],{},"6",[602,1631,1632],{},[1181,1633,1634],{},"3",[794,1636,803],{},[1625,1638,1639,1647],{},[599,1640,1641,1643],{},[1181,1642,1629],{},[602,1644,1645],{},[1181,1646,1634],{},[599,1648,1649,1653,1655],{},[602,1650,1651],{},[1181,1652,1634],{},[794,1654,796],{},[602,1656,1657],{},[1181,1658,1634],{},[794,1660,803],{},[1625,1662,1663,1671],{},[599,1664,1665,1667],{},[1181,1666,1629],{},[602,1668,1669],{},[1181,1670,1634],{},[1181,1672,1634],{},[794,1674,803],{},[1181,1676,1183],{},[602,1678,1679],{},[1181,1680,1634],{},[609,1682,1683],{"encoding":611},"\\frac{6}{\\sqrt{3}} = \\frac{6\\sqrt{3}}{\\sqrt{3} \\cdot \\sqrt{3}} = \\frac{6\\sqrt{3}}{3} = 2\\sqrt{3}",[583,1685,1687,1822,2048,2175],{"className":1686,"ariaHidden":617},[616],[583,1688,1690,1694,1813,1816,1819],{"className":1689},[621],[583,1691],{"className":1692,"style":1693},[625],"height:2.2514em;vertical-align:-0.93em;",[583,1695,1697,1702,1809],{"className":1696},[630],[583,1698],{"className":1699},[1700,1701],"mopen","nulldelimiter",[583,1703,1705],{"className":1704},[1625],[583,1706,1708,1800],{"className":1707},[635,636],[583,1709,1711,1797],{"className":1710},[640],[583,1712,1715,1774,1785],{"className":1713,"style":1714},[644],"height:1.3214em;",[583,1716,1718,1721],{"style":1717},"top:-2.2028em;",[583,1719],{"className":1720,"style":655},[654],[583,1722,1724],{"className":1723},[630],[583,1725,1727],{"className":1726},[630,631],[583,1728,1730,1765],{"className":1729},[635,636],[583,1731,1733,1762],{"className":1732},[640],[583,1734,1737,1749],{"className":1735,"style":1736},[644],"height:0.9072em;",[583,1738,1740,1743],{"className":1739,"style":650},[649],[583,1741],{"className":1742,"style":655},[654],[583,1744,1746],{"className":1745,"style":659},[630],[583,1747,1634],{"className":1748},[630],[583,1750,1752,1755],{"style":1751},"top:-2.8672em;",[583,1753],{"className":1754,"style":655},[654],[583,1756,1758],{"className":1757,"style":674},[673],[676,1759,1760],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,1761],{"d":686},[583,1763,691],{"className":1764},[690],[583,1766,1768],{"className":1767},[640],[583,1769,1772],{"className":1770,"style":1771},[644],"height:0.1328em;",[583,1773],{},[583,1775,1777,1780],{"style":1776},"top:-3.23em;",[583,1778],{"className":1779,"style":655},[654],[583,1781],{"className":1782,"style":1784},[1783],"frac-line","border-bottom-width:0.04em;",[583,1786,1788,1791],{"style":1787},"top:-3.677em;",[583,1789],{"className":1790,"style":655},[654],[583,1792,1794],{"className":1793},[630],[583,1795,1629],{"className":1796},[630],[583,1798,691],{"className":1799},[690],[583,1801,1803],{"className":1802},[640],[583,1804,1807],{"className":1805,"style":1806},[644],"height:0.93em;",[583,1808],{},[583,1810],{"className":1811},[1812,1701],"mclose",[583,1814],{"className":1815,"style":933},[868],[583,1817,803],{"className":1818},[937],[583,1820],{"className":1821,"style":933},[868],[583,1823,1825,1829,2039,2042,2045],{"className":1824},[621],[583,1826],{"className":1827,"style":1828},[625],"height:2.5142em;vertical-align:-0.93em;",[583,1830,1832,1835,2036],{"className":1831},[630],[583,1833],{"className":1834},[1700,1701],[583,1836,1838],{"className":1837},[1625],[583,1839,1841,2028],{"className":1840},[635,636],[583,1842,1844,2025],{"className":1843},[640],[583,1845,1848,1959,1967],{"className":1846,"style":1847},[644],"height:1.5842em;",[583,1849,1850,1853],{"style":1717},[583,1851],{"className":1852,"style":655},[654],[583,1854,1856,1903,1906,1909,1912],{"className":1855},[630],[583,1857,1859],{"className":1858},[630,631],[583,1860,1862,1895],{"className":1861},[635,636],[583,1863,1865,1892],{"className":1864},[640],[583,1866,1868,1880],{"className":1867,"style":1736},[644],[583,1869,1871,1874],{"className":1870,"style":650},[649],[583,1872],{"className":1873,"style":655},[654],[583,1875,1877],{"className":1876,"style":659},[630],[583,1878,1634],{"className":1879},[630],[583,1881,1882,1885],{"style":1751},[583,1883],{"className":1884,"style":655},[654],[583,1886,1888],{"className":1887,"style":674},[673],[676,1889,1890],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,1891],{"d":686},[583,1893,691],{"className":1894},[690],[583,1896,1898],{"className":1897},[640],[583,1899,1901],{"className":1900,"style":1771},[644],[583,1902],{},[583,1904],{"className":1905,"style":869},[868],[583,1907,796],{"className":1908},[873],[583,1910],{"className":1911,"style":869},[868],[583,1913,1915],{"className":1914},[630,631],[583,1916,1918,1951],{"className":1917},[635,636],[583,1919,1921,1948],{"className":1920},[640],[583,1922,1924,1936],{"className":1923,"style":1736},[644],[583,1925,1927,1930],{"className":1926,"style":650},[649],[583,1928],{"className":1929,"style":655},[654],[583,1931,1933],{"className":1932,"style":659},[630],[583,1934,1634],{"className":1935},[630],[583,1937,1938,1941],{"style":1751},[583,1939],{"className":1940,"style":655},[654],[583,1942,1944],{"className":1943,"style":674},[673],[676,1945,1946],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,1947],{"d":686},[583,1949,691],{"className":1950},[690],[583,1952,1954],{"className":1953},[640],[583,1955,1957],{"className":1956,"style":1771},[644],[583,1958],{},[583,1960,1961,1964],{"style":1776},[583,1962],{"className":1963,"style":655},[654],[583,1965],{"className":1966,"style":1784},[1783],[583,1968,1969,1972],{"style":1787},[583,1970],{"className":1971,"style":655},[654],[583,1973,1975,1978],{"className":1974},[630],[583,1976,1629],{"className":1977},[630],[583,1979,1981],{"className":1980},[630,631],[583,1982,1984,2017],{"className":1983},[635,636],[583,1985,1987,2014],{"className":1986},[640],[583,1988,1990,2002],{"className":1989,"style":1736},[644],[583,1991,1993,1996],{"className":1992,"style":650},[649],[583,1994],{"className":1995,"style":655},[654],[583,1997,1999],{"className":1998,"style":659},[630],[583,2000,1634],{"className":2001},[630],[583,2003,2004,2007],{"style":1751},[583,2005],{"className":2006,"style":655},[654],[583,2008,2010],{"className":2009,"style":674},[673],[676,2011,2012],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,2013],{"d":686},[583,2015,691],{"className":2016},[690],[583,2018,2020],{"className":2019},[640],[583,2021,2023],{"className":2022,"style":1771},[644],[583,2024],{},[583,2026,691],{"className":2027},[690],[583,2029,2031],{"className":2030},[640],[583,2032,2034],{"className":2033,"style":1806},[644],[583,2035],{},[583,2037],{"className":2038},[1812,1701],[583,2040],{"className":2041,"style":933},[868],[583,2043,803],{"className":2044},[937],[583,2046],{"className":2047,"style":933},[868],[583,2049,2051,2055,2166,2169,2172],{"className":2050},[621],[583,2052],{"className":2053,"style":2054},[625],"height:2.2702em;vertical-align:-0.686em;",[583,2056,2058,2061,2163],{"className":2057},[630],[583,2059],{"className":2060},[1700,1701],[583,2062,2064],{"className":2063},[1625],[583,2065,2067,2154],{"className":2066},[635,636],[583,2068,2070,2151],{"className":2069},[640],[583,2071,2073,2085,2093],{"className":2072,"style":1847},[644],[583,2074,2076,2079],{"style":2075},"top:-2.314em;",[583,2077],{"className":2078,"style":655},[654],[583,2080,2082],{"className":2081},[630],[583,2083,1634],{"className":2084},[630],[583,2086,2087,2090],{"style":1776},[583,2088],{"className":2089,"style":655},[654],[583,2091],{"className":2092,"style":1784},[1783],[583,2094,2095,2098],{"style":1787},[583,2096],{"className":2097,"style":655},[654],[583,2099,2101,2104],{"className":2100},[630],[583,2102,1629],{"className":2103},[630],[583,2105,2107],{"className":2106},[630,631],[583,2108,2110,2143],{"className":2109},[635,636],[583,2111,2113,2140],{"className":2112},[640],[583,2114,2116,2128],{"className":2115,"style":1736},[644],[583,2117,2119,2122],{"className":2118,"style":650},[649],[583,2120],{"className":2121,"style":655},[654],[583,2123,2125],{"className":2124,"style":659},[630],[583,2126,1634],{"className":2127},[630],[583,2129,2130,2133],{"style":1751},[583,2131],{"className":2132,"style":655},[654],[583,2134,2136],{"className":2135,"style":674},[673],[676,2137,2138],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,2139],{"d":686},[583,2141,691],{"className":2142},[690],[583,2144,2146],{"className":2145},[640],[583,2147,2149],{"className":2148,"style":1771},[644],[583,2150],{},[583,2152,691],{"className":2153},[690],[583,2155,2157],{"className":2156},[640],[583,2158,2161],{"className":2159,"style":2160},[644],"height:0.686em;",[583,2162],{},[583,2164],{"className":2165},[1812,1701],[583,2167],{"className":2168,"style":933},[868],[583,2170,803],{"className":2171},[937],[583,2173],{"className":2174,"style":933},[868],[583,2176,2178,2182,2185],{"className":2177},[621],[583,2179],{"className":2180,"style":2181},[625],"height:1.04em;vertical-align:-0.0839em;",[583,2183,1183],{"className":2184},[630],[583,2186,2188],{"className":2187},[630,631],[583,2189,2191,2226],{"className":2190},[635,636],[583,2192,2194,2223],{"className":2193},[640],[583,2195,2198,2210],{"className":2196,"style":2197},[644],"height:0.9561em;",[583,2199,2201,2204],{"className":2200,"style":650},[649],[583,2202],{"className":2203,"style":655},[654],[583,2205,2207],{"className":2206,"style":659},[630],[583,2208,1634],{"className":2209},[630],[583,2211,2213,2216],{"style":2212},"top:-2.9161em;",[583,2214],{"className":2215,"style":655},[654],[583,2217,2219],{"className":2218,"style":674},[673],[676,2220,2221],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,2222],{"d":686},[583,2224,691],{"className":2225},[690],[583,2227,2229],{"className":2228},[640],[583,2230,2233],{"className":2231,"style":2232},[644],"height:0.0839em;",[583,2234],{},[583,2236,2238],{"className":2237},[1610],[583,2239,2241,2364],{"className":2240},[586],[583,2242,2244],{"className":2243},[590],[592,2245,2246],{"xmlns":594,"display":1619},[596,2247,2248,2361],{},[599,2249,2250,2267,2269,2321,2323,2351,2353,2357,2359],{},[1625,2251,2252,2255],{},[1181,2253,2254],{},"4",[599,2256,2257,2262,2264],{},[602,2258,2259],{},[1181,2260,2261],{},"5",[794,2263,973],{},[1181,2265,2266],{},"1",[794,2268,803],{},[1625,2270,2271,2291],{},[599,2272,2273,2275],{},[1181,2274,2254],{},[599,2276,2277,2280,2284,2286,2288],{},[794,2278,2279],{"fence":617},"(",[602,2281,2282],{},[1181,2283,2261],{},[794,2285,1074],{},[1181,2287,2266],{},[794,2289,2290],{"fence":617},")",[599,2292,2293,2307],{},[599,2294,2295,2297,2301,2303,2305],{},[794,2296,2279],{"fence":617},[602,2298,2299],{},[1181,2300,2261],{},[794,2302,973],{},[1181,2304,2266],{},[794,2306,2290],{"fence":617},[599,2308,2309,2311,2315,2317,2319],{},[794,2310,2279],{"fence":617},[602,2312,2313],{},[1181,2314,2261],{},[794,2316,1074],{},[1181,2318,2266],{},[794,2320,2290],{"fence":617},[794,2322,803],{},[1625,2324,2325,2343],{},[599,2326,2327,2329],{},[1181,2328,2254],{},[599,2330,2331,2333,2337,2339,2341],{},[794,2332,2279],{"fence":617},[602,2334,2335],{},[1181,2336,2261],{},[794,2338,1074],{},[1181,2340,2266],{},[794,2342,2290],{"fence":617},[599,2344,2345,2347,2349],{},[1181,2346,2261],{},[794,2348,1074],{},[1181,2350,2266],{},[794,2352,803],{},[602,2354,2355],{},[1181,2356,2261],{},[794,2358,1074],{},[1181,2360,2266],{},[609,2362,2363],{"encoding":611},"\\frac{4}{\\sqrt{5} 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einer Differenz im Nenner erweitert man mit der Summe:",[583,3056,3058],{"className":3057},[1610],[583,3059,3061,3171],{"className":3060},[586],[583,3062,3064],{"className":3063},[590],[592,3065,3066],{"xmlns":594,"display":1619},[596,3067,3068,3168],{},[599,3069,3070,3084,3086,3128,3130,3151,3153],{},[1625,3071,3072,3074],{},[1181,3073,2266],{},[599,3075,3076,3078,3080],{},[1181,3077,1634],{},[794,3079,1074],{},[602,3081,3082],{},[1181,3083,1183],{},[794,3085,803],{},[1625,3087,3088,3098],{},[599,3089,3090,3092,3094],{},[1181,3091,1634],{},[794,3093,973],{},[602,3095,3096],{},[1181,3097,1183],{},[599,3099,3100,3114],{},[599,3101,3102,3104,3106,3108,3112],{},[794,3103,2279],{"fence":617},[1181,3105,1634],{},[794,3107,1074],{},[602,3109,3110],{},[1181,3111,1183],{},[794,3113,2290],{"fence":617},[599,3115,3116,3118,3120,3122,3126],{},[794,3117,2279],{"fence":617},[1181,3119,1634],{},[794,3121,973],{},[602,3123,3124],{},[1181,3125,1183],{},[794,3127,2290],{"fence":617},[794,3129,803],{},[1625,3131,3132,3142],{},[599,3133,3134,3136,3138],{},[1181,3135,1634],{},[794,3137,973],{},[602,3139,3140],{},[1181,3141,1183],{},[599,3143,3144,3147,3149],{},[1181,3145,3146],{},"9",[794,3148,1074],{},[1181,3150,1183],{},[794,3152,803],{},[1625,3154,3155,3165],{},[599,3156,3157,3159,3161],{},[1181,3158,1634],{},[794,3160,973],{},[602,3162,3163],{},[1181,3164,1183],{},[1181,3166,3167],{},"7",[609,3169,3170],{"encoding":611},"\\frac{1}{3 - \\sqrt{2}} = \\frac{3 + \\sqrt{2}}{\\left(3 - \\sqrt{2}\\right)\\left(3 + \\sqrt{2}\\right)} = \\frac{3 + \\sqrt{2}}{9 - 2} = \\frac{3 + \\sqrt{2}}{7}",[583,3172,3174,3307,3589,3735],{"className":3173,"ariaHidden":617},[616],[583,3175,3177,3180,3298,3301,3304],{"className":3176},[621],[583,3178],{"className":3179,"style":1693},[625],[583,3181,3183,3186,3295],{"className":3182},[630],[583,3184],{"className":3185},[1700,1701],[583,3187,3189],{"className":3188},[1625],[583,3190,3192,3287],{"className":3191},[635,636],[583,3193,3195,3284],{"className":3194},[640],[583,3196,3198,3265,3273],{"className":3197,"style":1714},[644],[583,3199,3200,3203],{"style":1717},[583,3201],{"className":3202,"style":655},[654],[583,3204,3206,3209,3212,3215,3218],{"className":3205},[630],[583,3207,1634],{"className":3208},[630],[583,3210],{"className":3211,"style":869},[868],[583,3213,1074],{"className":3214},[873],[583,3216],{"className":3217,"style":869},[868],[583,3219,3221],{"className":3220},[630,631],[583,3222,3224,3257],{"className":3223},[635,636],[583,3225,3227,3254],{"className":3226},[640],[583,3228,3230,3242],{"className":3229,"style":1736},[644],[583,3231,3233,3236],{"className":3232,"style":650},[649],[583,3234],{"className":3235,"style":655},[654],[583,3237,3239],{"className":3238,"style":659},[630],[583,3240,1183],{"className":3241},[630],[583,3243,3244,3247],{"style":1751},[583,3245],{"className":3246,"style":655},[654],[583,3248,3250],{"className":3249,"style":674},[673],[676,3251,3252],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,3253],{"d":686},[583,3255,691],{"className":3256},[690],[583,3258,3260],{"className":3259},[640],[583,3261,3263],{"className":3262,"style":1771},[644],[583,3264],{},[583,3266,3267,3270],{"style":1776},[583,3268],{"className":3269,"style":655},[654],[583,3271],{"className":3272,"style":1784},[1783],[583,3274,3275,3278],{"style":1787},[583,3276],{"className":3277,"style":655},[654],[583,3279,3281],{"className":3280},[630],[583,3282,2266],{"className":3283},[630],[583,3285,691],{"className":3286},[690],[583,3288,3290],{"className":3289},[640],[583,3291,3293],{"className":3292,"style":1806},[644],[583,3294],{},[583,3296],{"className":3297},[1812,1701],[583,3299],{"className":3300,"style":933},[868],[583,3302,803],{"className":3303},[937],[583,3305],{"className":3306,"style":933},[868],[583,3308,3310,3314,3580,3583,3586],{"className":3309},[621],[583,3311],{"className":3312,"style":3313},[625],"height:2.7315em;vertical-align:-1.1472em;",[583,3315,3317,3320,3577],{"className":3316},[630],[583,3318],{"className":3319},[1700,1701],[583,3321,3323],{"className":3322},[1625],[583,3324,3326,3569],{"className":3325},[635,636],[583,3327,3329,3566],{"className":3328},[640],[583,3330,3332,3491,3499],{"className":3331,"style":1847},[644],[583,3333,3334,3337],{"style":1717},[583,3335],{"className":3336,"style":655},[654],[583,3338,3340,3414,3417],{"className":3339},[630],[583,3341,3343,3349,3352,3355,3358,3361,3408],{"className":3342},[2537],[583,3344,3346],{"className":3345,"style":2542},[1700,2541],[583,3347,2279],{"className":3348},[2546,2547],[583,3350,1634],{"className":3351},[630],[583,3353],{"className":3354,"style":869},[868],[583,3356,1074],{"className":3357},[873],[583,3359],{"className":3360,"style":869},[868],[583,3362,3364],{"className":3363},[630,631],[583,3365,3367,3400],{"className":3366},[635,636],[583,3368,3370,3397],{"className":3369},[640],[583,3371,3373,3385],{"className":3372,"style":1736},[644],[583,3374,3376,3379],{"className":3375,"style":650},[649],[583,3377],{"className":3378,"style":655},[654],[583,3380,3382],{"className":3381,"style":659},[630],[583,3383,1183],{"className":3384},[630],[583,3386,3387,3390],{"style":1751},[583,3388],{"className":3389,"style":655},[654],[583,3391,3393],{"className":3392,"style":674},[673],[676,3394,3395],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,3396],{"d":686},[583,3398,691],{"className":3399},[690],[583,3401,3403],{"className":3402},[640],[583,3404,3406],{"className":3405,"style":1771},[644],[583,3407],{},[583,3409,3411],{"className":3410,"style":2542},[1812,2541],[583,3412,2290],{"className":3413},[2546,2547],[583,3415],{"className":3416,"style":2616},[868],[583,3418,3420,3426,3429,3432,3435,3438,3485],{"className":3419},[2537],[583,3421,3423],{"className":3422,"style":2542},[1700,2541],[583,3424,2279],{"className":3425},[2546,2547],[583,3427,1634],{"className":3428},[630],[583,3430],{"className":3431,"style":869},[868],[583,3433,973],{"className":3434},[873],[583,3436],{"className":3437,"style":869},[868],[583,3439,3441],{"className":3440},[630,631],[583,3442,3444,3477],{"className":3443},[635,636],[583,3445,3447,3474],{"className":3446},[640],[583,3448,3450,3462],{"className":3449,"style":1736},[644],[583,3451,3453,3456],{"className":3452,"style":650},[649],[583,3454],{"className":3455,"style":655},[654],[583,3457,3459],{"className":3458,"style":659},[630],[583,3460,1183],{"className":3461},[630],[583,3463,3464,3467],{"style":1751},[583,3465],{"className":3466,"style":655},[654],[583,3468,3470],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Wurzeln im Nenner:",[583,3863,3865],{"className":3864},[1610],[583,3866,3868,3940],{"className":3867},[586],[583,3869,3871],{"className":3870},[590],[592,3872,3873],{"xmlns":594,"display":1619},[596,3874,3875,3937],{},[599,3876,3877,3893,3895,3925,3927,3931,3933],{},[1625,3878,3879,3881],{},[1181,3880,2261],{},[599,3882,3883,3887,3889],{},[602,3884,3885],{},[1181,3886,3167],{},[794,3888,1074],{},[602,3890,3891],{},[1181,3892,1183],{},[794,3894,803],{},[1625,3896,3897,3917],{},[599,3898,3899,3901],{},[1181,3900,2261],{},[599,3902,3903,3905,3909,3911,3915],{},[794,3904,2279],{"fence":617},[602,3906,3907],{},[1181,3908,3167],{},[794,3910,973],{},[602,3912,3913],{},[1181,3914,1183],{},[794,3916,2290],{"fence":617},[599,3918,3919,3921,3923],{},[1181,3920,3167],{},[794,3922,1074],{},[1181,3924,1183],{},[794,3926,803],{},[602,3928,3929],{},[1181,3930,3167],{},[794,3932,973],{},[602,3934,3935],{},[1181,3936,1183],{},[609,3938,3939],{"encoding":611},"\\frac{5}{\\sqrt{7} - \\sqrt{2}} = \\frac{5\\left(\\sqrt{7} + \\sqrt{2}\\right)}{7 - 2} = \\sqrt{7} + \\sqrt{2}",[583,3941,3943,4120,4330,4392],{"className":3942,"ariaHidden":617},[616],[583,3944,3946,3949,4111,4114,4117],{"className":3945},[621],[583,3947],{"className":3948,"style":1693},[625],[583,3950,3952,3955,4108],{"className":3951},[630],[583,3953],{"className":3954},[1700,1701],[583,3956,3958],{"className":3957},[1625],[583,3959,3961,4100],{"className":3960},[635,636],[583,3962,3964,4097],{"className":3963},[640],[583,3965,3967,4078,4086],{"className":3966,"style":1714},[644],[583,3968,3969,3972],{"style":1717},[583,3970],{"className":3971,"style":655},[654],[583,3973,3975,4022,4025,4028,4031],{"className":3974},[630],[583,3976,3978],{"className":3977},[630,631],[583,3979,3981,4014],{"className":3980},[635,636],[583,3982,3984,4011],{"className":3983},[640],[583,3985,3987,3999],{"className":3986,"style":1736},[644],[583,3988,3990,3993],{"className":3989,"style":650},[649],[583,3991],{"className":3992,"style":655},[654],[583,3994,3996],{"className":3995,"style":659},[630],[583,3997,3167],{"className":3998},[630],[583,4000,4001,4004],{"style":1751},[583,4002],{"className":4003,"style":655},[654],[583,4005,4007],{"className":4006,"style":674},[673],[676,4008,4009],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,4010],{"d":686},[583,4012,691],{"className":4013},[690],[583,4015,4017],{"className":4016},[640],[583,4018,4020],{"className":4019,"style":1771},[644],[583,4021],{},[583,4023],{"className":4024,"style":869},[868],[583,4026,1074],{"className":4027},[873],[583,4029],{"className":4030,"style":869},[868],[583,4032,4034],{"className":4033},[630,631],[583,4035,4037,4070],{"className":4036},[635,636],[583,4038,4040,4067],{"className":4039},[640],[583,4041,4043,4055],{"className":4042,"style":1736},[644],[583,4044,4046,4049],{"className":4045,"style":650},[649],[583,4047],{"className":4048,"style":655},[654],[583,4050,4052],{"className":4051,"style":659},[630],[583,4053,1183],{"className":4054},[630],[583,4056,4057,4060],{"style":1751},[583,4058],{"className":4059,"style":655},[654],[583,4061,4063],{"className":4062,"style":674},[673],[676,4064,4065],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,4066],{"d":686},[583,4068,691],{"className":4069},[690],[583,4071,4073],{"className":4072},[640],[583,4074,4076],{"className":4075,"style":1771},[644],[583,4077],{},[583,4079,4080,4083],{"style":1776},[583,4081],{"className":4082,"style":655},[654],[583,4084],{"className":4085,"style":1784},[1783],[583,4087,4088,4091],{"style":1787},[583,4089],{"className":4090,"style":655},[654],[583,4092,4094],{"className":4093},[630],[583,4095,2261],{"className":4096},[630],[583,4098,691],{"className":4099},[690],[583,4101,4103],{"className":4102},[640],[583,4104,4106],{"className":4105,"style":1806},[644],[583,4107],{},[583,4109],{"className":4110},[1812,1701],[583,4112],{"className":4113,"style":933},[868],[583,4115,803],{"className":4116},[937],[583,4118],{"className":4119,"style":933},[868],[583,4121,4123,4126,4321,4324,4327],{"className":4122},[621],[583,4124],{"className":4125,"style":2818},[625],[583,4127,4129,4132,4318],{"className":4128},[630],[583,4130],{"className":4131},[1700,1701],[583,4133,4135],{"className":4134},[1625],[583,4136,4138,4310],{"className":4137},[635,636],[583,4139,4141,4307],{"className":4140},[640],[583,4142,4144,4167,4175],{"className":4143,"style":2525},[644],[583,4145,4146,4149],{"style":2075},[583,4147],{"className":4148,"style":655},[654],[583,4150,4152,4155,4158,4161,4164],{"className":4151},[630],[583,4153,3167],{"className":4154},[630],[583,4156],{"className":4157,"style":869},[868],[583,4159,1074],{"className":4160},[873],[583,4162],{"className":4163,"style":869},[868],[583,4165,1183],{"className":4166},[630],[583,4168,4169,4172],{"style":1776},[583,4170],{"className":4171,"style":655},[654],[583,4173],{"className":4174,"style":1784},[1783],[583,4176,4177,4180],{"style":2701},[583,4178],{"className":4179,"style":655},[654],[583,4181,4183,4186,4189],{"className":4182},[630],[583,4184,2261],{"className":4185},[630],[583,4187],{"className":4188,"style":2616},[868],[583,4190,4192,4198,4245,4248,4251,4254,4301],{"className":4191},[2537],[583,4193,4195],{"className":4194,"style":2542},[1700,2541],[583,4196,2279],{"className":4197},[2546,2547],[583,4199,4201],{"className":4200},[630,631],[583,4202,4204,4237],{"className":4203},[635,636],[583,4205,4207,4234],{"className":4206},[640],[583,4208,4210,4222],{"className":4209,"style":1736},[644],[583,4211,4213,4216],{"className":4212,"style":650},[649],[583,4214],{"className":4215,"style":655},[654],[583,4217,4219],{"className":4218,"style":659},[630],[583,4220,3167],{"className":4221},[630],[583,4223,4224,4227],{"style":1751},[583,4225],{"className":4226,"style":655},[654],[583,4228,4230],{"className":4229,"style":674},[673],[676,4231,4232],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,4233],{"d":686},[583,4235,691],{"className":4236},[690],[583,4238,4240],{"className":4239},[640],[583,4241,4243],{"className":4242,"style":1771},[644],[583,4244],{},[583,4246],{"className":4247,"style":869},[868],[583,4249,973],{"className":4250},[873],[583,4252],{"className":4253,"style":869},[868],[583,4255,4257],{"className":4256},[630,631],[583,4258,4260,4293],{"className":4259},[635,636],[583,4261,4263,4290],{"className":4262},[640],[583,4264,4266,4278],{"className":4265,"style":1736},[644],[583,4267,4269,4272],{"className":4268,"style":650},[649],[583,4270],{"className":4271,"style":655},[654],[583,4273,4275],{"className":4274,"style":659},[630],[583,4276,1183],{"className":4277},[630],[583,4279,4280,4283],{"style":1751},[583,4281],{"className":4282,"style":655},[654],[583,4284,4286],{"className":4285,"style":674},[673],[676,4287,4288],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,4289],{"d":686},[583,4291,691],{"className":4292},[690],[583,4294,4296],{"className":4295},[640],[583,4297,4299],{"className":4298,"style":1771},[644],[583,4300],{},[583,4302,4304],{"className":4303,"style":2542},[1812,2541],[583,4305,2290],{"className":4306},[2546,2547],[583,4308,691],{"className":4309},[690],[583,4311,4313],{"className":4312},[640],[583,4314,4316],{"className":4315,"style":2965},[644],[583,4317],{},[583,4319],{"className":4320},[1812,1701],[583,4322],{"className":4323,"style":933},[868],[583,4325,803],{"className":4326},[937],[583,4328],{"className":4329,"style":933},[868],[583,4331,4333,4336,4383,4386,4389],{"className":4332},[621],[583,4334],{"className":4335,"style":2181},[625],[583,4337,4339],{"className":4338},[630,631],[583,4340,4342,4375],{"className":4341},[635,636],[583,4343,4345,4372],{"className":4344},[640],[583,4346,4348,4360],{"className":4347,"style":2197},[644],[583,4349,4351,4354],{"className":4350,"style":650},[649],[583,4352],{"className":4353,"style":655},[654],[583,4355,4357],{"className":4356,"style":659},[630],[583,4358,3167],{"className":4359},[630],[583,4361,4362,4365],{"style":2212},[583,4363],{"className":4364,"style":655},[654],[583,4366,4368],{"className":4367,"style":674},[673],[676,4369,4370],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,4371],{"d":686},[583,4373,691],{"className":4374},[690],[583,4376,4378],{"className":4377},[640],[583,4379,4381],{"className":4380,"style":2232},[644],[583,4382],{},[583,4384],{"className":4385,"style":869},[868],[583,4387,973],{"className":4388},[873],[583,4390],{"className":4391,"style":869},[868],[583,4393,4395,4398],{"className":4394},[621],[583,4396],{"className":4397,"style":2181},[625],[583,4399,4401],{"className":4400},[630,631],[583,4402,4404,4437],{"className":4403},[635,636],[583,4405,4407,4434],{"className":4406},[640],[583,4408,4410,4422],{"className":4409,"style":2197},[644],[583,4411,4413,4416],{"className":4412,"style":650},[649],[583,4414],{"className":4415,"style":655},[654],[583,4417,4419],{"className":4418,"style":659},[630],[583,4420,1183],{"className":4421},[630],[583,4423,4424,4427],{"style":2212},[583,4425],{"className":4426,"style":655},[654],[583,4428,4430],{"className":4429,"style":674},[673],[676,4431,4432],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,4433],{"d":686},[583,4435,691],{"className":4436},[690],[583,4438,4440],{"className":4439},[640],[583,4441,4443],{"className":4442,"style":2232},[644],[583,4444],{},[559,4446,4448],{"id":4447},"typische-fehler","Typische Fehler",[576,4450,4451,4458,4735],{},[579,4452,4453,4454,4457],{},"Nur den Nenner mit der Wurzel multiplizieren. Erweitern heißt: Zähler ",[568,4455,4456],{},"und"," Nenner mit demselben Term multiplizieren.",[579,4459,4460,4461,4734],{},"Bei einer Summe nur mit der Wurzel erweitern: ",[583,4462,4464,4506],{"className":4463},[586],[583,4465,4467],{"className":4466},[590],[592,4468,4469],{"xmlns":594},[596,4470,4471,4503],{},[599,4472,4473,4487,4489,4493,4495,4497,4499],{},[599,4474,4475,4477,4481,4483,4485],{},[794,4476,2279],{"fence":617},[602,4478,4479],{},[1181,4480,2261],{},[794,4482,973],{},[1181,4484,2266],{},[794,4486,2290],{"fence":617},[794,4488,796],{},[602,4490,4491],{},[1181,4492,2261],{},[794,4494,803],{},[1181,4496,2261],{},[794,4498,973],{},[602,4500,4501],{},[1181,4502,2261],{},[609,4504,4505],{"encoding":611},"\\left(\\sqrt{5} + 1\\right) \\cdot \\sqrt{5} = 5 + \\sqrt{5}",[583,4507,4509,4599,4662,4681],{"className":4508,"ariaHidden":617},[616],[583,4510,4512,4516,4590,4593,4596],{"className":4511},[621],[583,4513],{"className":4514,"style":4515},[625],"height:1.2572em;vertical-align:-0.35em;",[583,4517,4519,4525,4572,4575,4578,4581,4584],{"className":4518},[2537],[583,4520,4522],{"className":4521,"style":2542},[1700,2541],[583,4523,2279],{"className":4524},[2546,2547],[583,4526,4528],{"className":4527},[630,631],[583,4529,4531,4564],{"className":4530},[635,636],[583,4532,4534,4561],{"className":4533},[640],[583,4535,4537,4549],{"className":4536,"style":1736},[644],[583,4538,4540,4543],{"className":4539,"style":650},[649],[583,4541],{"className":4542,"style":655},[654],[583,4544,4546],{"className":4545,"style":659},[630],[583,4547,2261],{"className":4548},[630],[583,4550,4551,4554],{"style":1751},[583,4552],{"className":4553,"style":655},[654],[583,4555,4557],{"className":4556,"style":674},[673],[676,4558,4559],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,4560],{"d":686},[583,4562,691],{"className":4563},[690],[583,4565,4567],{"className":4566},[640],[583,4568,4570],{"className":4569,"style":1771},[644],[583,4571],{},[583,4573],{"className":4574,"style":869},[868],[583,4576,973],{"className":4577},[873],[583,4579],{"className":4580,"style":869},[868],[583,4582,2266],{"className":4583},[630],[583,4585,4587],{"className":4586,"style":2542},[1812,2541],[583,4588,2290],{"className":4589},[2546,2547],[583,4591],{"className":4592,"style":869},[868],[583,4594,796],{"className":4595},[873],[583,4597],{"className":4598,"style":869},[868],[583,4600,4602,4606,4653,4656,4659],{"className":4601},[621],[583,4603],{"className":4604,"style":4605},[625],"height:1.04em;vertical-align:-0.1328em;",[583,4607,4609],{"className":4608},[630,631],[583,4610,4612,4645],{"className":4611},[635,636],[583,4613,4615,4642],{"className":4614},[640],[583,4616,4618,4630],{"className":4617,"style":1736},[644],[583,4619,4621,4624],{"className":4620,"style":650},[649],[583,4622],{"className":4623,"style":655},[654],[583,4625,4627],{"className":4626,"style":659},[630],[583,4628,2261],{"className":4629},[630],[583,4631,4632,4635],{"style":1751},[583,4633],{"className":4634,"style":655},[654],[583,4636,4638],{"className":4637,"style":674},[673],[676,4639,4640],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,4641],{"d":686},[583,4643,691],{"className":4644},[690],[583,4646,4648],{"className":4647},[640],[583,4649,4651],{"className":4650,"style":1771},[644],[583,4652],{},[583,4654],{"className":4655,"style":933},[868],[583,4657,803],{"className":4658},[937],[583,4660],{"className":4661,"style":933},[868],[583,4663,4665,4669,4672,4675,4678],{"className":4664},[621],[583,4666],{"className":4667,"style":4668},[625],"height:0.7278em;vertical-align:-0.0833em;",[583,4670,2261],{"className":4671},[630],[583,4673],{"className":4674,"style":869},[868],[583,4676,973],{"className":4677},[873],[583,4679],{"className":4680,"style":869},[868],[583,4682,4684,4687],{"className":4683},[621],[583,4685],{"className":4686,"style":4605},[625],[583,4688,4690],{"className":4689},[630,631],[583,4691,4693,4726],{"className":4692},[635,636],[583,4694,4696,4723],{"className":4695},[640],[583,4697,4699,4711],{"className":4698,"style":1736},[644],[583,4700,4702,4705],{"className":4701,"style":650},[649],[583,4703],{"className":4704,"style":655},[654],[583,4706,4708],{"className":4707,"style":659},[630],[583,4709,2261],{"className":4710},[630],[583,4712,4713,4716],{"style":1751},[583,4714],{"className":4715,"style":655},[654],[583,4717,4719],{"className":4718,"style":674},[673],[676,4720,4721],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,4722],{"d":686},[583,4724,691],{"className":4725},[690],[583,4727,4729],{"className":4728},[640],[583,4730,4732],{"className":4731,"style":1771},[644],[583,4733],{}," enthält immer noch eine Wurzel. Man braucht die dritte binomische Formel.",[579,4736,4737,4738,4818,4819,5088,5089,5140,5141,1252],{},"Den Nenner ",[583,4739,4741,4762],{"className":4740},[586],[583,4742,4744],{"className":4743},[590],[592,4745,4746],{"xmlns":594},[596,4747,4748,4760],{},[599,4749,4750,4752,4754],{},[605,4751,607],{},[794,4753,1074],{},[1176,4755,4756,4758],{},[605,4757,976],{},[1181,4759,1183],{},[609,4761,1186],{"encoding":611},[583,4763,4765,4783],{"className":4764,"ariaHidden":617},[616],[583,4766,4768,4771,4774,4777,4780],{"className":4767},[621],[583,4769],{"className":4770,"style":1196},[625],[583,4772,607],{"className":4773},[630,663],[583,4775],{"className":4776,"style":869},[868],[583,4778,1074],{"className":4779},[873],[583,4781],{"className":4782,"style":869},[868],[583,4784,4786,4789],{"className":4785},[621],[583,4787],{"className":4788,"style":1215},[625],[583,4790,4792,4795],{"className":4791},[630],[583,4793,976],{"className":4794},[630,663],[583,4796,4798],{"className":4797},[1225],[583,4799,4801],{"className":4800},[635],[583,4802,4804],{"className":4803},[640],[583,4805,4807],{"className":4806,"style":1215},[644],[583,4808,4809,4812],{"style":1237},[583,4810],{"className":4811,"style":1241},[654],[583,4813,4815],{"className":4814},[1245,1246,1247,1248],[583,4816,1183],{"className":4817},[630,1248]," falsch berechnen: ",[583,4820,4822,4874],{"className":4821},[586],[583,4823,4825],{"className":4824},[590],[592,4826,4827],{"xmlns":594},[596,4828,4829,4871],{},[599,4830,4831,4845,4859,4861,4863,4865,4867,4869],{},[599,4832,4833,4835,4837,4839,4843],{},[794,4834,2279],{"fence":617},[1181,4836,1634],{},[794,4838,1074],{},[602,4840,4841],{},[1181,4842,1183],{},[794,4844,2290],{"fence":617},[599,4846,4847,4849,4851,4853,4857],{},[794,4848,2279],{"fence":617},[1181,4850,1634],{},[794,4852,973],{},[602,4854,4855],{},[1181,4856,1183],{},[794,4858,2290],{"fence":617},[794,4860,803],{},[1181,4862,3146],{},[794,4864,1074],{},[1181,4866,1183],{},[794,4868,803],{},[1181,4870,3167],{},[609,4872,4873],{"encoding":611},"\\left(3 - \\sqrt{2}\\right)\\left(3 + \\sqrt{2}\\right) = 9 - 2 = 7",[583,4875,4877,5043,5061,5079],{"className":4876,"ariaHidden":617},[616],[583,4878,4880,4883,4957,4960,5034,5037,5040],{"className":4879},[621],[583,4881],{"className":4882,"style":4515},[625],[583,4884,4886,4892,4895,4898,4901,4904,4951],{"className":4885},[2537],[583,4887,4889],{"className":4888,"style":2542},[1700,2541],[583,4890,2279],{"className":4891},[2546,2547],[583,4893,1634],{"className":4894},[630],[583,4896],{"className":4897,"style":869},[868],[583,4899,1074],{"className":4900},[873],[583,4902],{"className":4903,"style":869},[868],[583,4905,4907],{"className":4906},[630,631],[583,4908,4910,4943],{"className":4909},[635,636],[583,4911,4913,4940],{"className":4912},[640],[583,4914,4916,4928],{"className":4915,"style":1736},[644],[583,4917,4919,4922],{"className":4918,"style":650},[649],[583,4920],{"className":4921,"style":655},[654],[583,4923,4925],{"className":4924,"style":659},[630],[583,4926,1183],{"className":4927},[630],[583,4929,4930,4933],{"style":1751},[583,4931],{"className":4932,"style":655},[654],[583,4934,4936],{"className":4935,"style":674},[673],[676,4937,4938],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,4939],{"d":686},[583,4941,691],{"className":4942},[690],[583,4944,4946],{"className":4945},[640],[583,4947,4949],{"className":4948,"style":1771},[644],[583,4950],{},[583,4952,4954],{"className":4953,"style":2542},[1812,2541],[583,4955,2290],{"className":4956},[2546,2547],[583,4958],{"className":4959,"style":2616},[868],[583,4961,4963,4969,4972,4975,4978,4981,5028],{"className":4962},[2537],[583,4964,4966],{"className":4965,"style":2542},[1700,2541],[583,4967,2279],{"className":4968},[2546,2547],[583,4970,1634],{"className":4971},[630],[583,4973],{"className":4974,"style":869},[868],[583,4976,973],{"className":4977},[873],[583,4979],{"className":4980,"style":869},[868],[583,4982,4984],{"className":4983},[630,631],[583,4985,4987,5020],{"className":4986},[635,636],[583,4988,4990,5017],{"className":4989},[640],[583,4991,4993,5005],{"className":4992,"style":1736},[644],[583,4994,4996,4999],{"className":4995,"style":650},[649],[583,4997],{"className":4998,"style":655},[654],[583,5000,5002],{"className":5001,"style":659},[630],[583,5003,1183],{"className":5004},[630],[583,5006,5007,5010],{"style":1751},[583,5008],{"className":5009,"style":655},[654],[583,5011,5013],{"className":5012,"style":674},[673],[676,5014,5015],{"xmlns":678,"width":679,"height":680,"viewBox":681,"preserveAspectRatio":682},[684,5016],{"d":686},[583,5018,691],{"className":5019},[690],[583,5021,5023],{"className":5022},[640],[583,5024,5026],{"className":5025,"style":1771},[644],[583,5027],{},[583,5029,5031],{"className":5030,"style":2542},[1812,2541],[583,5032,2290],{"className":5033},[2546,2547],[583,5035],{"className":5036,"style":933},[868],[583,5038,803],{"className":5039},[937],[583,5041],{"className":5042,"style":933},[868],[583,5044,5046,5049,5052,5055,5058],{"className":5045},[621],[583,5047],{"className":5048,"style":4668},[625],[583,5050,3146],{"className":5051},[630],[583,5053],{"className":5054,"style":869},[868],[583,5056,1074],{"className":5057},[873],[583,5059],{"className":5060,"style":869},[868],[583,5062,5064,5067,5070,5073,5076],{"className":5063},[621],[583,5065],{"className":5066,"style":3048},[625],[583,5068,1183],{"className":5069},[630],[583,5071],{"className":5072,"style":933},[868],[583,5074,803],{"className":5075},[937],[583,5077],{"className":5078,"style":933},[868],[583,5080,5082,5085],{"className":5081},[621],[583,5083],{"className":5084,"style":3048},[625],[583,5086,3167],{"className":5087},[630],", nicht ",[583,5090,5092,5110],{"className":5091},[586],[583,5093,5095],{"className":5094},[590],[592,5096,5097],{"xmlns":594},[596,5098,5099,5107],{},[599,5100,5101,5103,5105],{},[1181,5102,3146],{},[794,5104,1074],{},[1181,5106,2254],{},[609,5108,5109],{"encoding":611},"9 - 4",[583,5111,5113,5131],{"className":5112,"ariaHidden":617},[616],[583,5114,5116,5119,5122,5125,5128],{"className":5115},[621],[583,5117],{"className":5118,"style":4668},[625],[583,5120,3146],{"className":5121},[630],[583,5123],{"className":5124,"style":869},[868],[583,5126,1074],{"className":5127},[873],[583,5129],{"className":5130,"style":869},[868],[583,5132,5134,5137],{"className":5133},[621],[583,5135],{"className":5136,"style":3048},[625],[583,5138,2254],{"className":5139},[630]," oder ",[583,5142,5144,5162],{"className":5143},[586],[583,5145,5147],{"className":5146},[590],[592,5148,5149],{"xmlns":594},[596,5150,5151,5159],{},[599,5152,5153,5155,5157],{},[1181,5154,1634],{},[794,5156,1074],{},[1181,5158,1183],{},[609,5160,5161],{"encoding":611},"3 - 2",[583,5163,5165,5183],{"className":5164,"ariaHidden":617},[616],[583,5166,5168,5171,5174,5177,5180],{"className":5167},[621],[583,5169],{"className":5170,"style":4668},[625],[583,5172,1634],{"className":5173},[630],[583,5175],{"className":5176,"style":869},[868],[583,5178,1074],{"className":5179},[873],[583,5181],{"className":5182,"style":869},[868],[583,5184,5186,5189],{"className":5185},[621],[583,5187],{"className":5188,"style":3048},[625],[583,5190,1183],{"className":5191},[630],{"title":5193,"searchDepth":5194,"depth":5194,"links":5195},"",2,[5196,5197,5198],{"id":561,"depth":5194,"text":562},{"id":1605,"depth":5194,"text":1606},{"id":4447,"depth":5194,"text":4448},[5200,5203,5207,5210,5213,5216,5219,5221,5224],{"lhs":5201,"rhs":5202},"a\u002Fsqrt(b)","a*sqrt(b)\u002Fb",{"lhs":5204,"rhs":5205,"where":5206},"a\u002F(sqrt(b) + c)","a*(sqrt(b) - c)\u002F(b - c^2)",{"c":5194},{"lhs":5204,"rhs":5205,"where":5208},{"c":5209},-0.25,{"lhs":5211,"rhs":5212},"6\u002Fsqrt(3)","2*sqrt(3)",{"lhs":5214,"rhs":5215},"4\u002F(sqrt(5) + 1)","sqrt(5) - 1",{"lhs":5217,"rhs":5218},"1\u002F(3 - sqrt(2))","(3 + sqrt(2))\u002F7",{"lhs":5220,"rhs":3167},"(3 - sqrt(2))*(3 + sqrt(2))",{"lhs":5222,"rhs":5223},"5\u002F(sqrt(7) - sqrt(2))","sqrt(7) + sqrt(2)",{"lhs":5225,"rhs":5226},"(sqrt(5) + 1)*sqrt(5)","5 + sqrt(5)","b > 0,\\ b \\neq c^2","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b > 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmsup>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b \\neq c^2\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8141em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","rationalizing-denominator","\\frac{a}{\\sqrt{b}} = \\frac{a\\sqrt{b}}{b}, \\qquad \\frac{a}{\\sqrt{b} + c} = \\frac{a\\left(\\sqrt{b} - c\\right)}{b - c^2}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmfrac>\u003Cmi>a\u003C\u002Fmi>\u003Cmsqrt>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmsqrt>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmsqrt>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmsqrt>\u003C\u002Fmrow>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmfrac>\u003Cmi>a\u003C\u002Fmi>\u003Cmrow>\u003Cmsqrt>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmsqrt>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmsqrt>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmsqrt>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmsup>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\frac{a}{\\sqrt{b}} = \\frac{a\\sqrt{b}}{b}, \\qquad \\frac{a}{\\sqrt{b} + c} = \\frac{a\\left(\\sqrt{b} - c\\right)}{b - c^2}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0376em;vertical-align:-0.93em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.1778em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord sqrt\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9322em;\">\u003Cspan class=\"svg-align\" style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\" style=\"padding-left:0.833em;\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.8922em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"hide-tail\" style=\"min-width:0.853em;height:1.08em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"400em\" height=\"1.08em\" viewBox=\"0 0 400000 1080\" preserveAspectRatio=\"xMinYMin slice\">\u003Cpath d=\"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" 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