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ist für jedes Quadrat gleich: Die Diagonale ist immer gut ",[573,1124,1126,1149],{"className":1125},[576],[573,1127,1129],{"className":1128},[580],[582,1130,1131],{"xmlns":584},[586,1132,1133,1146],{},[589,1134,1135,1138,1142],{},[685,1136,1137],{},"41",[1139,1140,1141],"mtext",{}," ",[592,1143,1145],{"mathvariant":1144},"normal","%",[596,1147,1148],{"encoding":598},"41\\,\\%",[573,1150,1152],{"className":1151,"ariaHidden":603},[602],[573,1153,1155,1159,1162,1166],{"className":1154},[607],[573,1156],{"className":1157,"style":1158},[611],"height:0.8056em;vertical-align:-0.0556em;",[573,1160,1137],{"className":1161},[616],[573,1163],{"className":1164,"style":1165},[720],"margin-right:0.1667em;",[573,1167,1145],{"className":1168},[616]," länger als die Seite.",[559,1171,1173],{"id":1172},"herleitung","Herleitung",[564,1175,1176],{},"Mit dem Satz des Pythagoras im halben Quadrat:",[573,1178,1180],{"className":1179},[656],[573,1181,1183,1261],{"className":1182},[576],[573,1184,1186],{"className":1185},[580],[582,1187,1188],{"xmlns":584,"display":665},[586,1189,1190,1258],{},[589,1191,1192,1199,1201,1207,1210,1216,1218,1220,1226,1229,1232,1234,1236,1238,1250,1252,1254],{},[1193,1194,1195,1197],"msup",{},[592,1196,633],{},[685,1198,687],{},[673,1200,675],{},[1193,1202,1203,1205],{},[592,1204,594],{},[685,1206,687],{},[673,1208,1209],{},"+",[1193,1211,1212,1214],{},[592,1213,594],{},[685,1215,687],{},[673,1217,675],{},[685,1219,687],{},[1193,1221,1222,1224],{},[592,1223,594],{},[685,1225,687],{},[720,1227],{"width":1228},"1em",[673,1230,1231],{},"⇒",[720,1233],{"width":1228},[592,1235,633],{},[673,1237,675],{},[682,1239,1240],{},[589,1241,1242,1244],{},[685,1243,687],{},[1193,1245,1246,1248],{},[592,1247,594],{},[685,1249,687],{},[673,1251,675],{},[592,1253,594],{},[682,1255,1256],{},[685,1257,687],{},[596,1259,1260],{"encoding":598},"d^2 = a^2 + a^2 = 2a^2 \\quad\\Rightarrow\\quad d = \\sqrt{2a^2} = a \\sqrt{2}",[573,1262,1264,1316,1363,1407,1461,1479,1576],{"className":1263,"ariaHidden":603},[602],[573,1265,1267,1271,1307,1310,1313],{"className":1266},[607],[573,1268],{"className":1269,"style":1270},[611],"height:0.8641em;",[573,1272,1274,1277],{"className":1273},[616],[573,1275,633],{"className":1276},[616,617],[573,1278,1281],{"className":1279},[1280],"msupsub",[573,1282,1284],{"className":1283},[750],[573,1285,1287],{"className":1286},[755],[573,1288,1290],{"className":1289,"style":1270},[759],[573,1291,1293,1297],{"style":1292},"top:-3.113em;margin-right:0.05em;",[573,1294],{"className":1295,"style":1296},[767],"height:2.7em;",[573,1298,1304],{"className":1299},[1300,1301,1302,1303],"sizing","reset-size6","size3","mtight",[573,1305,687],{"className":1306},[616,1303],[573,1308],{"className":1309,"style":721},[720],[573,1311,675],{"className":1312},[725],[573,1314],{"className":1315,"style":721},[720],[573,1317,1319,1323,1352,1356,1360],{"className":1318},[607],[573,1320],{"className":1321,"style":1322},[611],"height:0.9474em;vertical-align:-0.0833em;",[573,1324,1326,1329],{"className":1325},[616],[573,1327,594],{"className":1328},[616,617],[573,1330,1332],{"className":1331},[1280],[573,1333,1335],{"className":1334},[750],[573,1336,1338],{"className":1337},[755],[573,1339,1341],{"className":1340,"style":1270},[759],[573,1342,1343,1346],{"style":1292},[573,1344],{"className":1345,"style":1296},[767],[573,1347,1349],{"className":1348},[1300,1301,1302,1303],[573,1350,687],{"className":1351},[616,1303],[573,1353],{"className":1354,"style":1355},[720],"margin-right:0.2222em;",[573,1357,1209],{"className":1358},[1359],"mbin",[573,1361],{"className":1362,"style":1355},[720],[573,1364,1366,1369,1398,1401,1404],{"className":1365},[607],[573,1367],{"className":1368,"style":1270},[611],[573,1370,1372,1375],{"className":1371},[616],[573,1373,594],{"className":1374},[616,617],[573,1376,1378],{"className":1377},[1280],[573,1379,1381],{"className":1380},[750],[573,1382,1384],{"className":1383},[755],[573,1385,1387],{"className":1386,"style":1270},[759],[573,1388,1389,1392],{"style":1292},[573,1390],{"className":1391,"style":1296},[767],[573,1393,1395],{"className":1394},[1300,1301,1302,1303],[573,1396,687],{"className":1397},[616,1303],[573,1399],{"className":1400,"style":721},[720],[573,1402,675],{"className":1403},[725],[573,1405],{"className":1406,"style":721},[720],[573,1408,1410,1413,1416,1445,1449,1452,1455,1458],{"className":1409},[607],[573,1411],{"className":1412,"style":1270},[611],[573,1414,687],{"className":1415},[616],[573,1417,1419,1422],{"className":1418},[616],[573,1420,594],{"className":1421},[616,617],[573,1423,1425],{"className":1424},[1280],[573,1426,1428],{"className":1427},[750],[573,1429,1431],{"className":1430},[755],[573,1432,1434],{"className":1433,"style":1270},[759],[573,1435,1436,1439],{"style":1292},[573,1437],{"className":1438,"style":1296},[767],[573,1440,1442],{"className":1441},[1300,1301,1302,1303],[573,1443,687],{"className":1444},[616,1303],[573,1446],{"className":1447,"style":1448},[720],"margin-right:1em;",[573,1450],{"className":1451,"style":721},[720],[573,1453,1231],{"className":1454},[725],[573,1456],{"className":1457,"style":1448},[720],[573,1459],{"className":1460,"style":721},[720],[573,1462,1464,1467,1470,1473,1476],{"className":1463},[607],[573,1465],{"className":1466,"style":645},[611],[573,1468,633],{"className":1469},[616,617],[573,1471],{"className":1472,"style":721},[720],[573,1474,675],{"className":1475},[725],[573,1477],{"className":1478,"style":721},[720],[573,1480,1482,1486,1567,1570,1573],{"className":1481},[607],[573,1483],{"className":1484,"style":1485},[611],"height:1.04em;vertical-align:-0.0361em;",[573,1487,1489],{"className":1488},[616,775],[573,1490,1492,1558],{"className":1491},[750,751],[573,1493,1495,1555],{"className":1494},[755],[573,1496,1499,1542],{"className":1497,"style":1498},[759],"height:1.0039em;",[573,1500,1502,1505],{"className":1501,"style":790},[789],[573,1503],{"className":1504,"style":768},[767],[573,1506,1508,1511],{"className":1507,"style":797},[616],[573,1509,687],{"className":1510},[616],[573,1512,1514,1517],{"className":1513},[616],[573,1515,594],{"className":1516},[616,617],[573,1518,1520],{"className":1519},[1280],[573,1521,1523],{"className":1522},[750],[573,1524,1526],{"className":1525},[755],[573,1527,1530],{"className":1528,"style":1529},[759],"height:0.7401em;",[573,1531,1533,1536],{"style":1532},"top:-2.989em;margin-right:0.05em;",[573,1534],{"className":1535,"style":1296},[767],[573,1537,1539],{"className":1538},[1300,1301,1302,1303],[573,1540,687],{"className":1541},[616,1303],[573,1543,1545,1548],{"style":1544},"top:-2.9639em;",[573,1546],{"className":1547,"style":768},[767],[573,1549,1551],{"className":1550,"style":811},[810],[813,1552,1553],{"xmlns":815,"width":816,"height":817,"viewBox":818,"preserveAspectRatio":819},[821,1554],{"d":823},[573,1556,828],{"className":1557},[827],[573,1559,1561],{"className":1560},[755],[573,1562,1565],{"className":1563,"style":1564},[759],"height:0.0361em;",[573,1566],{},[573,1568],{"className":1569,"style":721},[720],[573,1571,675],{"className":1572},[725],[573,1574],{"className":1575,"style":721},[720],[573,1577,1579,1583,1586],{"className":1578},[607],[573,1580],{"className":1581,"style":1582},[611],"height:1.04em;vertical-align:-0.0839em;",[573,1584,594],{"className":1585},[616,617],[573,1587,1589],{"className":1588},[616,775],[573,1590,1592,1627],{"className":1591},[750,751],[573,1593,1595,1624],{"className":1594},[755],[573,1596,1599,1611],{"className":1597,"style":1598},[759],"height:0.9561em;",[573,1600,1602,1605],{"className":1601,"style":790},[789],[573,1603],{"className":1604,"style":768},[767],[573,1606,1608],{"className":1607,"style":797},[616],[573,1609,687],{"className":1610},[616],[573,1612,1614,1617],{"style":1613},"top:-2.9161em;",[573,1615],{"className":1616,"style":768},[767],[573,1618,1620],{"className":1619,"style":811},[810],[813,1621,1622],{"xmlns":815,"width":816,"height":817,"viewBox":818,"preserveAspectRatio":819},[821,1623],{"d":823},[573,1625,828],{"className":1626},[827],[573,1628,1630],{"className":1629},[755],[573,1631,1634],{"className":1632,"style":1633},[759],"height:0.0839em;",[573,1635],{},[559,1637,1639],{"id":1638},"beispiele","Beispiele",[564,1641,1642,1643,1689],{},"Ein Quadrat hat die Seitenlänge ",[573,1644,1646,1666],{"className":1645},[576],[573,1647,1649],{"className":1648},[580],[582,1650,1651],{"xmlns":584},[586,1652,1653,1663],{},[589,1654,1655,1658,1660],{},[685,1656,1657],{},"5",[1139,1659,1141],{},[1139,1661,1662],{},"cm",[596,1664,1665],{"encoding":598},"5\\,\\text{cm}",[573,1667,1669],{"className":1668,"ariaHidden":603},[602],[573,1670,1672,1676,1679,1682],{"className":1671},[607],[573,1673],{"className":1674,"style":1675},[611],"height:0.6444em;",[573,1677,1657],{"className":1678},[616],[573,1680],{"className":1681,"style":1165},[720],[573,1683,1686],{"className":1684},[616,1685],"text",[573,1687,1662],{"className":1688},[616],":",[573,1691,1693],{"className":1692},[656],[573,1694,1696,1742],{"className":1695},[576],[573,1697,1699],{"className":1698},[580],[582,1700,1701],{"xmlns":584,"display":665},[586,1702,1703,1739],{},[589,1704,1705,1707,1709,1711,1715,1717,1719,1721,1726,1728,1730,1732,1735,1737],{},[592,1706,633],{},[673,1708,675],{},[685,1710,1657],{},[682,1712,1713],{},[685,1714,687],{},[1139,1716,1141],{},[1139,1718,1662],{},[673,1720,675],{},[682,1722,1723],{},[685,1724,1725],{},"50",[1139,1727,1141],{},[1139,1729,1662],{},[673,1731,1026],{},[685,1733,1734],{},"7,07",[1139,1736,1141],{},[1139,1738,1662],{},[596,1740,1741],{"encoding":598},"d = 5 \\sqrt{2}\\,\\text{cm} = \\sqrt{50}\\,\\text{cm} \\approx 7{,}07\\,\\text{cm}",[573,1743,1745,1763,1837,1908],{"className":1744,"ariaHidden":603},[602],[573,1746,1748,1751,1754,1757,1760],{"className":1747},[607],[573,1749],{"className":1750,"style":645},[611],[573,1752,633],{"className":1753},[616,617],[573,1755],{"className":1756,"style":721},[720],[573,1758,675],{"className":1759},[725],[573,1761],{"className":1762,"style":721},[720],[573,1764,1766,1769,1772,1819,1822,1828,1831,1834],{"className":1765},[607],[573,1767],{"className":1768,"style":1582},[611],[573,1770,1657],{"className":1771},[616],[573,1773,1775],{"className":1774},[616,775],[573,1776,1778,1811],{"className":1777},[750,751],[573,1779,1781,1808],{"className":1780},[755],[573,1782,1784,1796],{"className":1783,"style":1598},[759],[573,1785,1787,1790],{"className":1786,"style":790},[789],[573,1788],{"className":1789,"style":768},[767],[573,1791,1793],{"className":1792,"style":797},[616],[573,1794,687],{"className":1795},[616],[573,1797,1798,1801],{"style":1613},[573,1799],{"className":1800,"style":768},[767],[573,1802,1804],{"className":1803,"style":811},[810],[813,1805,1806],{"xmlns":815,"width":816,"height":817,"viewBox":818,"preserveAspectRatio":819},[821,1807],{"d":823},[573,1809,828],{"className":1810},[827],[573,1812,1814],{"className":1813},[755],[573,1815,1817],{"className":1816,"style":1633},[759],[573,1818],{},[573,1820],{"className":1821,"style":1165},[720],[573,1823,1825],{"className":1824},[616,1685],[573,1826,1662],{"className":1827},[616],[573,1829],{"className":1830,"style":721},[720],[573,1832,675],{"className":1833},[725],[573,1835],{"className":1836,"style":721},[720],[573,1838,1840,1843,1890,1893,1899,1902,1905],{"className":1839},[607],[573,1841],{"className":1842,"style":1582},[611],[573,1844,1846],{"className":1845},[616,775],[573,1847,1849,1882],{"className":1848},[750,751],[573,1850,1852,1879],{"className":1851},[755],[573,1853,1855,1867],{"className":1854,"style":1598},[759],[573,1856,1858,1861],{"className":1857,"style":790},[789],[573,1859],{"className":1860,"style":768},[767],[573,1862,1864],{"className":1863,"style":797},[616],[573,1865,1725],{"className":1866},[616],[573,1868,1869,1872],{"style":1613},[573,1870],{"className":1871,"style":768},[767],[573,1873,1875],{"className":1874,"style":811},[810],[813,1876,1877],{"xmlns":815,"width":816,"height":817,"viewBox":818,"preserveAspectRatio":819},[821,1878],{"d":823},[573,1880,828],{"className":1881},[827],[573,1883,1885],{"className":1884},[755],[573,1886,1888],{"className":1887,"style":1633},[759],[573,1889],{},[573,1891],{"className":1892,"style":1165},[720],[573,1894,1896],{"className":1895},[616,1685],[573,1897,1662],{"className":1898},[616],[573,1900],{"className":1901,"style":721},[720],[573,1903,1026],{"className":1904},[725],[573,1906],{"className":1907,"style":721},[720],[573,1909,1911,1914,1918,1924,1928,1931],{"className":1910},[607],[573,1912],{"className":1913,"style":1105},[611],[573,1915,1917],{"className":1916},[616],"7",[573,1919,1921],{"className":1920},[616],[573,1922,1117],{"className":1923},[1116],[573,1925,1927],{"className":1926},[616],"07",[573,1929],{"className":1930,"style":1165},[720],[573,1932,1934],{"className":1933},[616,1685],[573,1935,1662],{"className":1936},[616],[564,1938,1939,1940,1984],{},"Die Diagonale eines quadratischen Tisches ist ",[573,1941,1943,1963],{"className":1942},[576],[573,1944,1946],{"className":1945},[580],[582,1947,1948],{"xmlns":584},[586,1949,1950,1960],{},[589,1951,1952,1955,1957],{},[685,1953,1954],{},"12",[1139,1956,1141],{},[1139,1958,1959],{},"dm",[596,1961,1962],{"encoding":598},"12\\,\\text{dm}",[573,1964,1966],{"className":1965,"ariaHidden":603},[602],[573,1967,1969,1972,1975,1978],{"className":1968},[607],[573,1970],{"className":1971,"style":645},[611],[573,1973,1954],{"className":1974},[616],[573,1976],{"className":1977,"style":1165},[720],[573,1979,1981],{"className":1980},[616,1685],[573,1982,1959],{"className":1983},[616]," lang. Die Seitenlänge ist:",[573,1986,1988],{"className":1987},[656],[573,1989,1991,2041],{"className":1990},[576],[573,1992,1994],{"className":1993},[580],[582,1995,1996],{"xmlns":584,"display":665},[586,1997,1998,2038],{},[589,1999,2000,2002,2004,2012,2014,2016,2018,2021,2025,2027,2029,2031,2034,2036],{},[592,2001,594],{},[673,2003,675],{},[677,2005,2006,2008],{},[685,2007,1954],{},[682,2009,2010],{},[685,2011,687],{},[1139,2013,1141],{},[1139,2015,1959],{},[673,2017,675],{},[685,2019,2020],{},"6",[682,2022,2023],{},[685,2024,687],{},[1139,2026,1141],{},[1139,2028,1959],{},[673,2030,1026],{},[685,2032,2033],{},"8,49",[1139,2035,1141],{},[1139,2037,1959],{},[596,2039,2040],{"encoding":598},"a = \\frac{12}{\\sqrt{2}}\\,\\text{dm} = 6\\sqrt{2}\\,\\text{dm} \\approx 8{,}49\\,\\text{dm}",[573,2042,2044,2062,2194,2268],{"className":2043,"ariaHidden":603},[602],[573,2045,2047,2050,2053,2056,2059],{"className":2046},[607],[573,2048],{"className":2049,"style":612},[611],[573,2051,594],{"className":2052},[616,617],[573,2054],{"className":2055,"style":721},[720],[573,2057,675],{"className":2058},[725],[573,2060],{"className":2061,"style":721},[720],[573,2063,2065,2069,2176,2179,2185,2188,2191],{"className":2064},[607],[573,2066],{"className":2067,"style":2068},[611],"height:2.2514em;vertical-align:-0.93em;",[573,2070,2072,2075,2173],{"className":2071},[616],[573,2073],{"className":2074},[742,743],[573,2076,2078],{"className":2077},[677],[573,2079,2081,2165],{"className":2080},[750,751],[573,2082,2084,2162],{"className":2083},[755],[573,2085,2088,2143,2151],{"className":2086,"style":2087},[759],"height:1.3214em;",[573,2089,2090,2093],{"style":763},[573,2091],{"className":2092,"style":768},[767],[573,2094,2096],{"className":2095},[616],[573,2097,2099],{"className":2098},[616,775],[573,2100,2102,2135],{"className":2101},[750,751],[573,2103,2105,2132],{"className":2104},[755],[573,2106,2108,2120],{"className":2107,"style":785},[759],[573,2109,2111,2114],{"className":2110,"style":790},[789],[573,2112],{"className":2113,"style":768},[767],[573,2115,2117],{"className":2116,"style":797},[616],[573,2118,687],{"className":2119},[616],[573,2121,2122,2125],{"style":803},[573,2123],{"className":2124,"style":768},[767],[573,2126,2128],{"className":2127,"style":811},[810],[813,2129,2130],{"xmlns":815,"width":816,"height":817,"viewBox":818,"preserveAspectRatio":819},[821,2131],{"d":823},[573,2133,828],{"className":2134},[827],[573,2136,2138],{"className":2137},[755],[573,2139,2141],{"className":2140,"style":835},[759],[573,2142],{},[573,2144,2145,2148],{"style":840},[573,2146],{"className":2147,"style":768},[767],[573,2149],{"className":2150,"style":848},[847],[573,2152,2153,2156],{"style":851},[573,2154],{"className":2155,"style":768},[767],[573,2157,2159],{"className":2158},[616],[573,2160,1954],{"className":2161},[616],[573,2163,828],{"className":2164},[827],[573,2166,2168],{"className":2167},[755],[573,2169,2171],{"className":2170,"style":870},[759],[573,2172],{},[573,2174],{"className":2175},[876,743],[573,2177],{"className":2178,"style":1165},[720],[573,2180,2182],{"className":2181},[616,1685],[573,2183,1959],{"className":2184},[616],[573,2186],{"className":2187,"style":721},[720],[573,2189,675],{"className":2190},[725],[573,2192],{"className":2193,"style":721},[720],[573,2195,2197,2200,2203,2250,2253,2259,2262,2265],{"className":2196},[607],[573,2198],{"className":2199,"style":1582},[611],[573,2201,2020],{"className":2202},[616],[573,2204,2206],{"className":2205},[616,775],[573,2207,2209,2242],{"className":2208},[750,751],[573,2210,2212,2239],{"className":2211},[755],[573,2213,2215,2227],{"className":2214,"style":1598},[759],[573,2216,2218,2221],{"className":2217,"style":790},[789],[573,2219],{"className":2220,"style":768},[767],[573,2222,2224],{"className":2223,"style":797},[616],[573,2225,687],{"className":2226},[616],[573,2228,2229,2232],{"style":1613},[573,2230],{"className":2231,"style":768},[767],[573,2233,2235],{"className":2234,"style":811},[810],[813,2236,2237],{"xmlns":815,"width":816,"height":817,"viewBox":818,"preserveAspectRatio":819},[821,2238],{"d":823},[573,2240,828],{"className":2241},[827],[573,2243,2245],{"className":2244},[755],[573,2246,2248],{"className":2247,"style":1633},[759],[573,2249],{},[573,2251],{"className":2252,"style":1165},[720],[573,2254,2256],{"className":2255},[616,1685],[573,2257,1959],{"className":2258},[616],[573,2260],{"className":2261,"style":721},[720],[573,2263,1026],{"className":2264},[725],[573,2266],{"className":2267,"style":721},[720],[573,2269,2271,2275,2279,2285,2289,2292],{"className":2270},[607],[573,2272],{"className":2273,"style":2274},[611],"height:0.8889em;vertical-align:-0.1944em;",[573,2276,2278],{"className":2277},[616],"8",[573,2280,2282],{"className":2281},[616],[573,2283,1117],{"className":2284},[1116],[573,2286,2288],{"className":2287},[616],"49",[573,2290],{"className":2291,"style":1165},[720],[573,2293,2295],{"className":2294},[616,1685],[573,2296,1959],{"className":2297},[616],[559,2299,2301],{"id":2300},"typische-fehler","Typische Fehler",[2303,2304,2305,2404,3083],"ul",{},[2306,2307,2308,2364,2365,2403],"li",{},[573,2309,2311,2331],{"className":2310},[576],[573,2312,2314],{"className":2313},[580],[582,2315,2316],{"xmlns":584},[586,2317,2318,2328],{},[589,2319,2320,2322,2324,2326],{},[592,2321,633],{},[673,2323,675],{},[685,2325,687],{},[592,2327,594],{},[596,2329,2330],{"encoding":598},"d = 2a",[573,2332,2334,2352],{"className":2333,"ariaHidden":603},[602],[573,2335,2337,2340,2343,2346,2349],{"className":2336},[607],[573,2338],{"className":2339,"style":645},[611],[573,2341,633],{"className":2342},[616,617],[573,2344],{"className":2345,"style":721},[720],[573,2347,675],{"className":2348},[725],[573,2350],{"className":2351,"style":721},[720],[573,2353,2355,2358,2361],{"className":2354},[607],[573,2356],{"className":2357,"style":1675},[611],[573,2359,687],{"className":2360},[616],[573,2362,594],{"className":2363},[616,617]," rechnen. Die Diagonale ist kürzer als zwei Seiten, nämlich nur etwa ",[573,2366,2368,2382],{"className":2367},[576],[573,2369,2371],{"className":2370},[580],[582,2372,2373],{"xmlns":584},[586,2374,2375,2379],{},[589,2376,2377],{},[685,2378,1029],{},[596,2380,2381],{"encoding":598},"1{,}414",[573,2383,2385],{"className":2384,"ariaHidden":603},[602],[573,2386,2388,2391,2394,2400],{"className":2387},[607],[573,2389],{"className":2390,"style":1105},[611],[573,2392,1109],{"className":2393},[616],[573,2395,2397],{"className":2396},[616],[573,2398,1117],{"className":2399},[1116],[573,2401,1121],{"className":2402},[616],"-mal so lang wie eine Seite.",[2306,2405,2406,2407,2435,2436,2497,2498,2687,2688,2798,2799,2851,2852,3082],{},"Beim Pythagoras die Wurzel nur auf ",[573,2408,2410,2423],{"className":2409},[576],[573,2411,2413],{"className":2412},[580],[582,2414,2415],{"xmlns":584},[586,2416,2417,2421],{},[589,2418,2419],{},[685,2420,687],{},[596,2422,687],{"encoding":598},[573,2424,2426],{"className":2425,"ariaHidden":603},[602],[573,2427,2429,2432],{"className":2428},[607],[573,2430],{"className":2431,"style":1675},[611],[573,2433,687],{"className":2434},[616]," ziehen und ",[573,2437,2439,2457],{"className":2438},[576],[573,2440,2442],{"className":2441},[580],[582,2443,2444],{"xmlns":584},[586,2445,2446,2454],{},[589,2447,2448],{},[1193,2449,2450,2452],{},[592,2451,594],{},[685,2453,687],{},[596,2455,2456],{"encoding":598},"a^2",[573,2458,2460],{"className":2459,"ariaHidden":603},[602],[573,2461,2463,2467],{"className":2462},[607],[573,2464],{"className":2465,"style":2466},[611],"height:0.8141em;",[573,2468,2470,2473],{"className":2469},[616],[573,2471,594],{"className":2472},[616,617],[573,2474,2476],{"className":2475},[1280],[573,2477,2479],{"className":2478},[750],[573,2480,2482],{"className":2481},[755],[573,2483,2485],{"className":2484,"style":2466},[759],[573,2486,2488,2491],{"style":2487},"top:-3.063em;margin-right:0.05em;",[573,2489],{"className":2490,"style":1296},[767],[573,2492,2494],{"className":2493},[1300,1301,1302,1303],[573,2495,687],{"className":2496},[616,1303]," stehen lassen: ",[573,2499,2501,2533],{"className":2500},[576],[573,2502,2504],{"className":2503},[580],[582,2505,2506],{"xmlns":584},[586,2507,2508,2530],{},[589,2509,2510,2522,2524,2526],{},[682,2511,2512],{},[589,2513,2514,2516],{},[685,2515,687],{},[1193,2517,2518,2520],{},[592,2519,594],{},[685,2521,687],{},[673,2523,675],{},[592,2525,594],{},[682,2527,2528],{},[685,2529,687],{},[596,2531,2532],{"encoding":598},"\\sqrt{2a^2} = a\\sqrt{2}",[573,2534,2536,2631],{"className":2535,"ariaHidden":603},[602],[573,2537,2539,2543,2622,2625,2628],{"className":2538},[607],[573,2540],{"className":2541,"style":2542},[611],"height:1.04em;vertical-align:-0.0849em;",[573,2544,2546],{"className":2545},[616,775],[573,2547,2549,2613],{"className":2548},[750,751],[573,2550,2552,2610],{"className":2551},[755],[573,2553,2556,2597],{"className":2554,"style":2555},[759],"height:0.9551em;",[573,2557,2559,2562],{"className":2558,"style":790},[789],[573,2560],{"className":2561,"style":768},[767],[573,2563,2565,2568],{"className":2564,"style":797},[616],[573,2566,687],{"className":2567},[616],[573,2569,2571,2574],{"className":2570},[616],[573,2572,594],{"className":2573},[616,617],[573,2575,2577],{"className":2576},[1280],[573,2578,2580],{"className":2579},[750],[573,2581,2583],{"className":2582},[755],[573,2584,2586],{"className":2585,"style":1529},[759],[573,2587,2588,2591],{"style":1532},[573,2589],{"className":2590,"style":1296},[767],[573,2592,2594],{"className":2593},[1300,1301,1302,1303],[573,2595,687],{"className":2596},[616,1303],[573,2598,2600,2603],{"style":2599},"top:-2.9151em;",[573,2601],{"className":2602,"style":768},[767],[573,2604,2606],{"className":2605,"style":811},[810],[813,2607,2608],{"xmlns":815,"width":816,"height":817,"viewBox":818,"preserveAspectRatio":819},[821,2609],{"d":823},[573,2611,828],{"className":2612},[827],[573,2614,2616],{"className":2615},[755],[573,2617,2620],{"className":2618,"style":2619},[759],"height:0.0849em;",[573,2621],{},[573,2623],{"className":2624,"style":721},[720],[573,2626,675],{"className":2627},[725],[573,2629],{"className":2630,"style":721},[720],[573,2632,2634,2637,2640],{"className":2633},[607],[573,2635],{"className":2636,"style":1042},[611],[573,2638,594],{"className":2639},[616,617],[573,2641,2643],{"className":2642},[616,775],[573,2644,2646,2679],{"className":2645},[750,751],[573,2647,2649,2676],{"className":2648},[755],[573,2650,2652,2664],{"className":2651,"style":785},[759],[573,2653,2655,2658],{"className":2654,"style":790},[789],[573,2656],{"className":2657,"style":768},[767],[573,2659,2661],{"className":2660,"style":797},[616],[573,2662,687],{"className":2663},[616],[573,2665,2666,2669],{"style":803},[573,2667],{"className":2668,"style":768},[767],[573,2670,2672],{"className":2671,"style":811},[810],[813,2673,2674],{"xmlns":815,"width":816,"height":817,"viewBox":818,"preserveAspectRatio":819},[821,2675],{"d":823},[573,2677,828],{"className":2678},[827],[573,2680,2682],{"className":2681},[755],[573,2683,2685],{"className":2684,"style":835},[759],[573,2686],{},", nicht ",[573,2689,2691,2713],{"className":2690},[576],[573,2692,2694],{"className":2693},[580],[582,2695,2696],{"xmlns":584},[586,2697,2698,2710],{},[589,2699,2700,2706],{},[1193,2701,2702,2704],{},[592,2703,594],{},[685,2705,687],{},[682,2707,2708],{},[685,2709,687],{},[596,2711,2712],{"encoding":598},"a^2\\sqrt{2}",[573,2714,2716],{"className":2715,"ariaHidden":603},[602],[573,2717,2719,2722,2751],{"className":2718},[607],[573,2720],{"className":2721,"style":1042},[611],[573,2723,2725,2728],{"className":2724},[616],[573,2726,594],{"className":2727},[616,617],[573,2729,2731],{"className":2730},[1280],[573,2732,2734],{"className":2733},[750],[573,2735,2737],{"className":2736},[755],[573,2738,2740],{"className":2739,"style":2466},[759],[573,2741,2742,2745],{"style":2487},[573,2743],{"className":2744,"style":1296},[767],[573,2746,2748],{"className":2747},[1300,1301,1302,1303],[573,2749,687],{"className":2750},[616,1303],[573,2752,2754],{"className":2753},[616,775],[573,2755,2757,2790],{"className":2756},[750,751],[573,2758,2760,2787],{"className":2759},[755],[573,2761,2763,2775],{"className":2762,"style":785},[759],[573,2764,2766,2769],{"className":2765,"style":790},[789],[573,2767],{"className":2768,"style":768},[767],[573,2770,2772],{"className":2771,"style":797},[616],[573,2773,687],{"className":2774},[616],[573,2776,2777,2780],{"style":803},[573,2778],{"className":2779,"style":768},[767],[573,2781,2783],{"className":2782,"style":811},[810],[813,2784,2785],{"xmlns":815,"width":816,"height":817,"viewBox":818,"preserveAspectRatio":819},[821,2786],{"d":823},[573,2788,828],{"className":2789},[827],[573,2791,2793],{"className":2792},[755],[573,2794,2796],{"className":2795,"style":835},[759],[573,2797],{},". Für ",[573,2800,2802,2821],{"className":2801},[576],[573,2803,2805],{"className":2804},[580],[582,2806,2807],{"xmlns":584},[586,2808,2809,2818],{},[589,2810,2811,2813,2815],{},[592,2812,594],{},[673,2814,675],{},[685,2816,2817],{},"4",[596,2819,2820],{"encoding":598},"a = 4",[573,2822,2824,2842],{"className":2823,"ariaHidden":603},[602],[573,2825,2827,2830,2833,2836,2839],{"className":2826},[607],[573,2828],{"className":2829,"style":612},[611],[573,2831,594],{"className":2832},[616,617],[573,2834],{"className":2835,"style":721},[720],[573,2837,675],{"className":2838},[725],[573,2840],{"className":2841,"style":721},[720],[573,2843,2845,2848],{"className":2844},[607],[573,2846],{"className":2847,"style":1675},[611],[573,2849,2817],{"className":2850},[616],": ",[573,2853,2855,2895],{"className":2854},[576],[573,2856,2858],{"className":2857},[580],[582,2859,2860],{"xmlns":584},[586,2861,2862,2892],{},[589,2863,2864,2879,2881,2883,2887,2889],{},[682,2865,2866],{},[589,2867,2868,2870,2873],{},[685,2869,687],{},[673,2871,2872],{},"⋅",[1193,2874,2875,2877],{},[685,2876,2817],{},[685,2878,687],{},[673,2880,675],{},[685,2882,2817],{},[682,2884,2885],{},[685,2886,687],{},[673,2888,1026],{},[685,2890,2891],{},"5,66",[596,2893,2894],{"encoding":598},"\\sqrt{2 \\cdot 4^2} = 4\\sqrt{2} \\approx 5{,}66",[573,2896,2898,2998,3063],{"className":2897,"ariaHidden":603},[602],[573,2899,2901,2904,2989,2992,2995],{"className":2900},[607],[573,2902],{"className":2903,"style":2542},[611],[573,2905,2907],{"className":2906},[616,775],[573,2908,2910,2981],{"className":2909},[750,751],[573,2911,2913,2978],{"className":2912},[755],[573,2914,2916,2966],{"className":2915,"style":2555},[759],[573,2917,2919,2922],{"className":2918,"style":790},[789],[573,2920],{"className":2921,"style":768},[767],[573,2923,2925,2928,2931,2934,2937],{"className":2924,"style":797},[616],[573,2926,687],{"className":2927},[616],[573,2929],{"className":2930,"style":1355},[720],[573,2932,2872],{"className":2933},[1359],[573,2935],{"className":2936,"style":1355},[720],[573,2938,2940,2943],{"className":2939},[616],[573,2941,2817],{"className":2942},[616],[573,2944,2946],{"className":2945},[1280],[573,2947,2949],{"className":2948},[750],[573,2950,2952],{"className":2951},[755],[573,2953,2955],{"className":2954,"style":1529},[759],[573,2956,2957,2960],{"style":1532},[573,2958],{"className":2959,"style":1296},[767],[573,2961,2963],{"className":2962},[1300,1301,1302,1303],[573,2964,687],{"className":2965},[616,1303],[573,2967,2968,2971],{"style":2599},[573,2969],{"className":2970,"style":768},[767],[573,2972,2974],{"className":2973,"style":811},[810],[813,2975,2976],{"xmlns":815,"width":816,"height":817,"viewBox":818,"preserveAspectRatio":819},[821,2977],{"d":823},[573,2979,828],{"className":2980},[827],[573,2982,2984],{"className":2983},[755],[573,2985,2987],{"className":2986,"style":2619},[759],[573,2988],{},[573,2990],{"className":2991,"style":721},[720],[573,2993,675],{"className":2994},[725],[573,2996],{"className":2997,"style":721},[720],[573,2999,3001,3004,3007,3054,3057,3060],{"className":3000},[607],[573,3002],{"className":3003,"style":1042},[611],[573,3005,2817],{"className":3006},[616],[573,3008,3010],{"className":3009},[616,775],[573,3011,3013,3046],{"className":3012},[750,751],[573,3014,3016,3043],{"className":3015},[755],[573,3017,3019,3031],{"className":3018,"style":785},[759],[573,3020,3022,3025],{"className":3021,"style":790},[789],[573,3023],{"className":3024,"style":768},[767],[573,3026,3028],{"className":3027,"style":797},[616],[573,3029,687],{"className":3030},[616],[573,3032,3033,3036],{"style":803},[573,3034],{"className":3035,"style":768},[767],[573,3037,3039],{"className":3038,"style":811},[810],[813,3040,3041],{"xmlns":815,"width":816,"height":817,"viewBox":818,"preserveAspectRatio":819},[821,3042],{"d":823},[573,3044,828],{"className":3045},[827],[573,3047,3049],{"className":3048},[755],[573,3050,3052],{"className":3051,"style":835},[759],[573,3053],{},[573,3055],{"className":3056,"style":721},[720],[573,3058,1026],{"className":3059},[725],[573,3061],{"className":3062,"style":721},[720],[573,3064,3066,3069,3072,3078],{"className":3065},[607],[573,3067],{"className":3068,"style":1105},[611],[573,3070,1657],{"className":3071},[616],[573,3073,3075],{"className":3074},[616],[573,3076,1117],{"className":3077},[1116],[573,3079,3081],{"className":3080},[616],"66",".",[2306,3084,3085,3086,3161,3162,3236],{},"Beim Rückwärtsrechnen mit 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