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\\sqrt{3}}{3}",[573,908,910,928,1060],{"className":909,"ariaHidden":603},[602],[573,911,913,916,919,922,925],{"className":912},[607],[573,914],{"className":915,"style":612},[611],[573,917,594],{"className":918},[616,617],[573,920],{"className":921,"style":734},[733],[573,923,879],{"className":924},[738],[573,926],{"className":927,"style":734},[733],[573,929,931,935,1051,1054,1057],{"className":930},[607],[573,932],{"className":933,"style":934},[611],"height:2.3014em;vertical-align:-0.93em;",[573,936,938,943,1047],{"className":937},[616],[573,939],{"className":940},[941,942],"mopen","nulldelimiter",[573,944,946],{"className":945},[881],[573,947,949,1038],{"className":948},[665,666],[573,950,952,1035],{"className":951},[670],[573,953,956,1012,1023],{"className":954,"style":955},[674],"height:1.3714em;",[573,957,959,962],{"style":958},"top:-2.2028em;",[573,960],{"className":961,"style":685},[684],[573,963,965],{"className":964},[616],[573,966,968],{"className":967},[616,661],[573,969,971,1004],{"className":970},[665,666],[573,972,974,1001],{"className":973},[670],[573,975,977,989],{"className":976,"style":675},[674],[573,978,980,983],{"className":979,"style":680},[679],[573,981],{"className":982,"style":685},[684],[573,984,986],{"className":985,"style":689},[616],[573,987,637],{"className":988},[616],[573,990,991,994],{"style":695},[573,992],{"className":993,"style":685},[684],[573,995,997],{"className":996,"style":703},[702],[705,998,999],{"xmlns":707,"width":708,"height":709,"viewBox":710,"preserveAspectRatio":711},[713,1000],{"d":715},[573,1002,720],{"className":1003},[719],[573,1005,1007],{"className":1006},[670],[573,1008,1010],{"className":1009,"style":727},[674],[573,1011],{},[573,1013,1015,1018],{"style":1014},"top:-3.23em;",[573,1016],{"className":1017,"style":685},[684],[573,1019],{"className":1020,"style":1022},[1021],"frac-line","border-bottom-width:0.04em;",[573,1024,1026,1029],{"style":1025},"top:-3.677em;",[573,1027],{"className":1028,"style":685},[684],[573,1030,1032],{"className":1031},[616],[573,1033,885],{"className":1034},[616,617],[573,1036,720],{"className":1037},[719],[573,1039,1041],{"className":1040},[670],[573,1042,1045],{"className":1043,"style":1044},[674],"height:0.93em;",[573,1046],{},[573,1048],{"className":1049},[1050,942],"mclose",[573,1052],{"className":1053,"style":734},[733],[573,1055,879],{"className":1056},[738],[573,1058],{"className":1059,"style":734},[733],[573,1061,1063,1067],{"className":1062},[607],[573,1064],{"className":1065,"style":1066},[611],"height:2.2702em;vertical-align:-0.686em;",[573,1068,1070,1073,1176],{"className":1069},[616],[573,1071],{"className":1072},[941,942],[573,1074,1076],{"className":1075},[881],[573,1077,1079,1167],{"className":1078},[665,666],[573,1080,1082,1164],{"className":1081},[670],[573,1083,1086,1098,1106],{"className":1084,"style":1085},[674],"height:1.5842em;",[573,1087,1089,1092],{"style":1088},"top:-2.314em;",[573,1090],{"className":1091,"style":685},[684],[573,1093,1095],{"className":1094},[616],[573,1096,637],{"className":1097},[616],[573,1099,1100,1103],{"style":1014},[573,1101],{"className":1102,"style":685},[684],[573,1104],{"className":1105,"style":1022},[1021],[573,1107,1108,1111],{"style":1025},[573,1109],{"className":1110,"style":685},[684],[573,1112,1114,1117],{"className":1113},[616],[573,1115,885],{"className":1116},[616,617],[573,1118,1120],{"className":1119},[616,661],[573,1121,1123,1156],{"className":1122},[665,666],[573,1124,1126,1153],{"className":1125},[670],[573,1127,1129,1141],{"className":1128,"style":675},[674],[573,1130,1132,1135],{"className":1131,"style":680},[679],[573,1133],{"className":1134,"style":685},[684],[573,1136,1138],{"className":1137,"style":689},[616],[573,1139,637],{"className":1140},[616],[573,1142,1143,1146],{"style":695},[573,1144],{"className":1145,"style":685},[684],[573,1147,1149],{"className":1148,"style":703},[702],[705,1150,1151],{"xmlns":707,"width":708,"height":709,"viewBox":710,"preserveAspectRatio":711},[713,1152],{"d":715},[573,1154,720],{"className":1155},[719],[573,1157,1159],{"className":1158},[670],[573,1160,1162],{"className":1161,"style":727},[674],[573,1163],{},[573,1165,720],{"className":1166},[719],[573,1168,1170],{"className":1169},[670],[573,1171,1174],{"className":1172,"style":1173},[674],"height:0.686em;",[573,1175],{},[573,1177],{"className":1178},[1050,942],[559,1180,1182],{"id":1181},"herleitung","Herleitung",[564,1184,1185,1186,1265,1266,1294,1295,1324],{},"Die Flächendiagonale ",[573,1187,1189,1206],{"className":1188},[576],[573,1190,1192],{"className":1191},[580],[582,1193,1194],{"xmlns":584},[586,1195,1196,1204],{},[589,1197,1198,1200],{},[592,1199,594],{},[632,1201,1202],{},[635,1203,791],{},[596,1205,794],{"encoding":598},[573,1207,1209],{"className":1208,"ariaHidden":603},[602],[573,1210,1212,1215,1218],{"className":1211},[607],[573,1213],{"className":1214,"style":657},[611],[573,1216,594],{"className":1217},[616,617],[573,1219,1221],{"className":1220},[616,661],[573,1222,1224,1257],{"className":1223},[665,666],[573,1225,1227,1254],{"className":1226},[670],[573,1228,1230,1242],{"className":1229,"style":675},[674],[573,1231,1233,1236],{"className":1232,"style":680},[679],[573,1234],{"className":1235,"style":685},[684],[573,1237,1239],{"className":1238,"style":689},[616],[573,1240,791],{"className":1241},[616],[573,1243,1244,1247],{"style":695},[573,1245],{"className":1246,"style":685},[684],[573,1248,1250],{"className":1249,"style":703},[702],[705,1251,1252],{"xmlns":707,"width":708,"height":709,"viewBox":710,"preserveAspectRatio":711},[713,1253],{"d":715},[573,1255,720],{"className":1256},[719],[573,1258,1260],{"className":1259},[670],[573,1261,1263],{"className":1262,"style":727},[674],[573,1264],{},", eine senkrechte Kante ",[573,1267,1269,1282],{"className":1268},[576],[573,1270,1272],{"className":1271},[580],[582,1273,1274],{"xmlns":584},[586,1275,1276,1280],{},[589,1277,1278],{},[592,1279,594],{},[596,1281,594],{"encoding":598},[573,1283,1285],{"className":1284,"ariaHidden":603},[602],[573,1286,1288,1291],{"className":1287},[607],[573,1289],{"className":1290,"style":612},[611],[573,1292,594],{"className":1293},[616,617]," und die Raumdiagonale ",[573,1296,1298,1311],{"className":1297},[576],[573,1299,1301],{"className":1300},[580],[582,1302,1303],{"xmlns":584},[586,1304,1305,1309],{},[589,1306,1307],{},[592,1308,885],{},[596,1310,885],{"encoding":598},[573,1312,1314],{"className":1313,"ariaHidden":603},[602],[573,1315,1317,1321],{"className":1316},[607],[573,1318],{"className":1319,"style":1320},[611],"height:0.6944em;",[573,1322,885],{"className":1323},[616,617]," bilden ein rechtwinkliges Dreieck. Mit dem Satz des Pythagoras:",[573,1326,1328],{"className":1327},[861],[573,1329,1331,1424],{"className":1330},[576],[573,1332,1334],{"className":1333},[580],[582,1335,1336],{"xmlns":584,"display":870},[586,1337,1338,1421],{},[589,1339,1340,1347,1349,1353,1355,1359,1366,1369,1375,1377,1379,1385,1387,1393,1395,1397,1403,1406,1409,1411,1413,1415,1417],{},[1341,1342,1343,1345],"msup",{},[592,1344,885],{},[635,1346,791],{},[639,1348,879],{},[639,1350,1352],{"stretchy":1351},"false","(",[592,1354,594],{},[632,1356,1357],{},[635,1358,791],{},[1341,1360,1361,1364],{},[639,1362,1363],{"stretchy":1351},")",[635,1365,791],{},[639,1367,1368],{},"+",[1341,1370,1371,1373],{},[592,1372,594],{},[635,1374,791],{},[639,1376,879],{},[635,1378,791],{},[1341,1380,1381,1383],{},[592,1382,594],{},[635,1384,791],{},[639,1386,1368],{},[1341,1388,1389,1391],{},[592,1390,594],{},[635,1392,791],{},[639,1394,879],{},[635,1396,637],{},[1341,1398,1399,1401],{},[592,1400,594],{},[635,1402,791],{},[733,1404],{"width":1405},"1em",[639,1407,1408],{},"⇒",[733,1410],{"width":1405},[592,1412,885],{},[639,1414,879],{},[592,1416,594],{},[632,1418,1419],{},[635,1420,637],{},[596,1422,1423],{"encoding":598},"d^2 = (a\\sqrt{2})^2 + a^2 = 2a^2 + a^2 = 3a^2 \\quad\\Rightarrow\\quad d = a\\sqrt{3}",[573,1425,1427,1479,1582,1626,1674,1718,1772,1790],{"className":1426,"ariaHidden":603},[602],[573,1428,1430,1434,1470,1473,1476],{"className":1429},[607],[573,1431],{"className":1432,"style":1433},[611],"height:0.8641em;",[573,1435,1437,1440],{"className":1436},[616],[573,1438,885],{"className":1439},[616,617],[573,1441,1444],{"className":1442},[1443],"msupsub",[573,1445,1447],{"className":1446},[665],[573,1448,1450],{"className":1449},[670],[573,1451,1453],{"className":1452,"style":1433},[674],[573,1454,1456,1460],{"style":1455},"top:-3.113em;margin-right:0.05em;",[573,1457],{"className":1458,"style":1459},[684],"height:2.7em;",[573,1461,1467],{"className":1462},[1463,1464,1465,1466],"sizing","reset-size6","size3","mtight",[573,1468,791],{"className":1469},[616,1466],[573,1471],{"className":1472,"style":734},[733],[573,1474,879],{"className":1475},[738],[573,1477],{"className":1478,"style":734},[733],[573,1480,1482,1486,1489,1492,1542,1571,1575,1579],{"className":1481},[607],[573,1483],{"className":1484,"style":1485},[611],"height:1.2061em;vertical-align:-0.25em;",[573,1487,1352],{"className":1488},[941],[573,1490,594],{"className":1491},[616,617],[573,1493,1495],{"className":1494},[616,661],[573,1496,1498,1533],{"className":1497},[665,666],[573,1499,1501,1530],{"className":1500},[670],[573,1502,1505,1517],{"className":1503,"style":1504},[674],"height:0.9561em;",[573,1506,1508,1511],{"className":1507,"style":680},[679],[573,1509],{"className":1510,"style":685},[684],[573,1512,1514],{"className":1513,"style":689},[616],[573,1515,791],{"className":1516},[616],[573,1518,1520,1523],{"style":1519},"top:-2.9161em;",[573,1521],{"className":1522,"style":685},[684],[573,1524,1526],{"className":1525,"style":703},[702],[705,1527,1528],{"xmlns":707,"width":708,"height":709,"viewBox":710,"preserveAspectRatio":711},[713,1529],{"d":715},[573,1531,720],{"className":1532},[719],[573,1534,1536],{"className":1535},[670],[573,1537,1540],{"className":1538,"style":1539},[674],"height:0.0839em;",[573,1541],{},[573,1543,1545,1548],{"className":1544},[1050],[573,1546,1363],{"className":1547},[1050],[573,1549,1551],{"className":1550},[1443],[573,1552,1554],{"className":1553},[665],[573,1555,1557],{"className":1556},[670],[573,1558,1560],{"className":1559,"style":1433},[674],[573,1561,1562,1565],{"style":1455},[573,1563],{"className":1564,"style":1459},[684],[573,1566,1568],{"className":1567},[1463,1464,1465,1466],[573,1569,791],{"className":1570},[616,1466],[573,1572],{"className":1573,"style":1574},[733],"margin-right:0.2222em;",[573,1576,1368],{"className":1577},[1578],"mbin",[573,1580],{"className":1581,"style":1574},[733],[573,1583,1585,1588,1617,1620,1623],{"className":1584},[607],[573,1586],{"className":1587,"style":1433},[611],[573,1589,1591,1594],{"className":1590},[616],[573,1592,594],{"className":1593},[616,617],[573,1595,1597],{"className":1596},[1443],[573,1598,1600],{"className":1599},[665],[573,1601,1603],{"className":1602},[670],[573,1604,1606],{"className":1605,"style":1433},[674],[573,1607,1608,1611],{"style":1455},[573,1609],{"className":1610,"style":1459},[684],[573,1612,1614],{"className":1613},[1463,1464,1465,1466],[573,1615,791],{"className":1616},[616,1466],[573,1618],{"className":1619,"style":734},[733],[573,1621,879],{"className":1622},[738],[573,1624],{"className":1625,"style":734},[733],[573,1627,1629,1633,1636,1665,1668,1671],{"className":1628},[607],[573,1630],{"className":1631,"style":1632},[611],"height:0.9474em;vertical-align:-0.0833em;",[573,1634,791],{"className":1635},[616],[573,1637,1639,1642],{"className":1638},[616],[573,1640,594],{"className":1641},[616,617],[573,1643,1645],{"className":1644},[1443],[573,1646,1648],{"className":1647},[665],[573,1649,1651],{"className":1650},[670],[573,1652,1654],{"className":1653,"style":1433},[674],[573,1655,1656,1659],{"style":1455},[573,1657],{"className":1658,"style":1459},[684],[573,1660,1662],{"className":1661},[1463,1464,1465,1466],[573,1663,791],{"className":1664},[616,1466],[573,1666],{"className":1667,"style":1574},[733],[573,1669,1368],{"className":1670},[1578],[573,1672],{"className":1673,"style":1574},[733],[573,1675,1677,1680,1709,1712,1715],{"className":1676},[607],[573,1678],{"className":1679,"style":1433},[611],[573,1681,1683,1686],{"className":1682},[616],[573,1684,594],{"className":1685},[616,617],[573,1687,1689],{"className":1688},[1443],[573,1690,1692],{"className":1691},[665],[573,1693,1695],{"className":1694},[670],[573,1696,1698],{"className":1697,"style":1433},[674],[573,1699,1700,1703],{"style":1455},[573,1701],{"className":1702,"style":1459},[684],[573,1704,1706],{"className":1705},[1463,1464,1465,1466],[573,1707,791],{"className":1708},[616,1466],[573,1710],{"className":1711,"style":734},[733],[573,1713,879],{"className":1714},[738],[573,1716],{"className":1717,"style":734},[733],[573,1719,1721,1724,1727,1756,1760,1763,1766,1769],{"className":1720},[607],[573,1722],{"className":1723,"style":1433},[611],[573,1725,637],{"className":1726},[616],[573,1728,1730,1733],{"className":1729},[616],[573,1731,594],{"className":1732},[616,617],[573,1734,1736],{"className":1735},[1443],[573,1737,1739],{"className":1738},[665],[573,1740,1742],{"className":1741},[670],[573,1743,1745],{"className":1744,"style":1433},[674],[573,1746,1747,1750],{"style":1455},[573,1748],{"className":1749,"style":1459},[684],[573,1751,1753],{"className":1752},[1463,1464,1465,1466],[573,1754,791],{"className":1755},[616,1466],[573,1757],{"className":1758,"style":1759},[733],"margin-right:1em;",[573,1761],{"className":1762,"style":734},[733],[573,1764,1408],{"className":1765},[738],[573,1767],{"className":1768,"style":1759},[733],[573,1770],{"className":1771,"style":734},[733],[573,1773,1775,1778,1781,1784,1787],{"className":1774},[607],[573,1776],{"className":1777,"style":1320},[611],[573,1779,885],{"className":1780},[616,617],[573,1782],{"className":1783,"style":734},[733],[573,1785,879],{"className":1786},[738],[573,1788],{"className":1789,"style":734},[733],[573,1791,1793,1797,1800],{"className":1792},[607],[573,1794],{"className":1795,"style":1796},[611],"height:1.04em;vertical-align:-0.0839em;",[573,1798,594],{"className":1799},[616,617],[573,1801,1803],{"className":1802},[616,661],[573,1804,1806,1839],{"className":1805},[665,666],[573,1807,1809,1836],{"className":1808},[670],[573,1810,1812,1824],{"className":1811,"style":1504},[674],[573,1813,1815,1818],{"className":1814,"style":680},[679],[573,1816],{"className":1817,"style":685},[684],[573,1819,1821],{"className":1820,"style":689},[616],[573,1822,637],{"className":1823},[616],[573,1825,1826,1829],{"style":1519},[573,1827],{"className":1828,"style":685},[684],[573,1830,1832],{"className":1831,"style":703},[702],[705,1833,1834],{"xmlns":707,"width":708,"height":709,"viewBox":710,"preserveAspectRatio":711},[713,1835],{"d":715},[573,1837,720],{"className":1838},[719],[573,1840,1842],{"className":1841},[670],[573,1843,1845],{"className":1844,"style":1539},[674],[573,1846],{},[559,1848,1850],{"id":1849},"beispiele","Beispiele",[564,1852,1853,1854,1903],{},"Ein Würfel hat die Kantenlänge ",[573,1855,1857,1879],{"className":1856},[576],[573,1858,1860],{"className":1859},[580],[582,1861,1862],{"xmlns":584},[586,1863,1864,1876],{},[589,1865,1866,1869,1873],{},[635,1867,1868],{},"4",[1870,1871,1872],"mtext",{}," ",[1870,1874,1875],{},"cm",[596,1877,1878],{"encoding":598},"4\\,\\text{cm}",[573,1880,1882],{"className":1881,"ariaHidden":603},[602],[573,1883,1885,1889,1892,1896],{"className":1884},[607],[573,1886],{"className":1887,"style":1888},[611],"height:0.6444em;",[573,1890,1868],{"className":1891},[616],[573,1893],{"className":1894,"style":1895},[733],"margin-right:0.1667em;",[573,1897,1900],{"className":1898},[616,1899],"text",[573,1901,1875],{"className":1902},[616],":",[573,1905,1907],{"className":1906},[861],[573,1908,1910,1956],{"className":1909},[576],[573,1911,1913],{"className":1912},[580],[582,1914,1915],{"xmlns":584,"display":870},[586,1916,1917,1953],{},[589,1918,1919,1921,1923,1925,1929,1931,1933,1935,1940,1942,1944,1946,1949,1951],{},[592,1920,885],{},[639,1922,879],{},[635,1924,1868],{},[632,1926,1927],{},[635,1928,637],{},[1870,1930,1872],{},[1870,1932,1875],{},[639,1934,879],{},[632,1936,1937],{},[635,1938,1939],{},"48",[1870,1941,1872],{},[1870,1943,1875],{},[639,1945,641],{},[635,1947,1948],{},"6,93",[1870,1950,1872],{},[1870,1952,1875],{},[596,1954,1955],{"encoding":598},"d = 4\\sqrt{3}\\,\\text{cm} = \\sqrt{48}\\,\\text{cm} \\approx 6{,}93\\,\\text{cm}",[573,1957,1959,1977,2051,2122],{"className":1958,"ariaHidden":603},[602],[573,1960,1962,1965,1968,1971,1974],{"className":1961},[607],[573,1963],{"className":1964,"style":1320},[611],[573,1966,885],{"className":1967},[616,617],[573,1969],{"className":1970,"style":734},[733],[573,1972,879],{"className":1973},[738],[573,1975],{"className":1976,"style":734},[733],[573,1978,1980,1983,1986,2033,2036,2042,2045,2048],{"className":1979},[607],[573,1981],{"className":1982,"style":1796},[611],[573,1984,1868],{"className":1985},[616],[573,1987,1989],{"className":1988},[616,661],[573,1990,1992,2025],{"className":1991},[665,666],[573,1993,1995,2022],{"className":1994},[670],[573,1996,1998,2010],{"className":1997,"style":1504},[674],[573,1999,2001,2004],{"className":2000,"style":680},[679],[573,2002],{"className":2003,"style":685},[684],[573,2005,2007],{"className":2006,"style":689},[616],[573,2008,637],{"className":2009},[616],[573,2011,2012,2015],{"style":1519},[573,2013],{"className":2014,"style":685},[684],[573,2016,2018],{"className":2017,"style":703},[702],[705,2019,2020],{"xmlns":707,"width":708,"height":709,"viewBox":710,"preserveAspectRatio":711},[713,2021],{"d":715},[573,2023,720],{"className":2024},[719],[573,2026,2028],{"className":2027},[670],[573,2029,2031],{"className":2030,"style":1539},[674],[573,2032],{},[573,2034],{"className":2035,"style":1895},[733],[573,2037,2039],{"className":2038},[616,1899],[573,2040,1875],{"className":2041},[616],[573,2043],{"className":2044,"style":734},[733],[573,2046,879],{"className":2047},[738],[573,2049],{"className":2050,"style":734},[733],[573,2052,2054,2057,2104,2107,2113,2116,2119],{"className":2053},[607],[573,2055],{"className":2056,"style":1796},[611],[573,2058,2060],{"className":2059},[616,661],[573,2061,2063,2096],{"className":2062},[665,666],[573,2064,2066,2093],{"className":2065},[670],[573,2067,2069,2081],{"className":2068,"style":1504},[674],[573,2070,2072,2075],{"className":2071,"style":680},[679],[573,2073],{"className":2074,"style":685},[684],[573,2076,2078],{"className":2077,"style":689},[616],[573,2079,1939],{"className":2080},[616],[573,2082,2083,2086],{"style":1519},[573,2084],{"className":2085,"style":685},[684],[573,2087,2089],{"className":2088,"style":703},[702],[705,2090,2091],{"xmlns":707,"width":708,"height":709,"viewBox":710,"preserveAspectRatio":711},[713,2092],{"d":715},[573,2094,720],{"className":2095},[719],[573,2097,2099],{"className":2098},[670],[573,2100,2102],{"className":2101,"style":1539},[674],[573,2103],{},[573,2105],{"className":2106,"style":1895},[733],[573,2108,2110],{"className":2109},[616,1899],[573,2111,1875],{"className":2112},[616],[573,2114],{"className":2115,"style":734},[733],[573,2117,641],{"className":2118},[738],[573,2120],{"className":2121,"style":734},[733],[573,2123,2125,2128,2132,2138,2142,2145],{"className":2124},[607],[573,2126],{"className":2127,"style":748},[611],[573,2129,2131],{"className":2130},[616],"6",[573,2133,2135],{"className":2134},[616],[573,2136,760],{"className":2137},[759],[573,2139,2141],{"className":2140},[616],"93",[573,2143],{"className":2144,"style":1895},[733],[573,2146,2148],{"className":2147},[616,1899],[573,2149,1875],{"className":2150},[616],[564,2152,2153,2154,2197],{},"Die Raumdiagonale eines Würfels ist ",[573,2155,2157,2176],{"className":2156},[576],[573,2158,2160],{"className":2159},[580],[582,2161,2162],{"xmlns":584},[586,2163,2164,2173],{},[589,2165,2166,2169,2171],{},[635,2167,2168],{},"9",[1870,2170,1872],{},[1870,2172,1875],{},[596,2174,2175],{"encoding":598},"9\\,\\text{cm}",[573,2177,2179],{"className":2178,"ariaHidden":603},[602],[573,2180,2182,2185,2188,2191],{"className":2181},[607],[573,2183],{"className":2184,"style":1888},[611],[573,2186,2168],{"className":2187},[616],[573,2189],{"className":2190,"style":1895},[733],[573,2192,2194],{"className":2193},[616,1899],[573,2195,1875],{"className":2196},[616]," lang. Die Kantenlänge ist:",[573,2199,2201],{"className":2200},[861],[573,2202,2204,2253],{"className":2203},[576],[573,2205,2207],{"className":2206},[580],[582,2208,2209],{"xmlns":584,"display":870},[586,2210,2211,2250],{},[589,2212,2213,2215,2217,2225,2227,2229,2231,2233,2237,2239,2241,2243,2246,2248],{},[592,2214,594],{},[639,2216,879],{},[881,2218,2219,2221],{},[635,2220,2168],{},[632,2222,2223],{},[635,2224,637],{},[1870,2226,1872],{},[1870,2228,1875],{},[639,2230,879],{},[635,2232,637],{},[632,2234,2235],{},[635,2236,637],{},[1870,2238,1872],{},[1870,2240,1875],{},[639,2242,641],{},[635,2244,2245],{},"5,20",[1870,2247,1872],{},[1870,2249,1875],{},[596,2251,2252],{"encoding":598},"a = \\frac{9}{\\sqrt{3}}\\,\\text{cm} = 3\\sqrt{3}\\,\\text{cm} \\approx 5{,}20\\,\\text{cm}",[573,2254,2256,2274,2406,2480],{"className":2255,"ariaHidden":603},[602],[573,2257,2259,2262,2265,2268,2271],{"className":2258},[607],[573,2260],{"className":2261,"style":612},[611],[573,2263,594],{"className":2264},[616,617],[573,2266],{"className":2267,"style":734},[733],[573,2269,879],{"className":2270},[738],[573,2272],{"className":2273,"style":734},[733],[573,2275,2277,2281,2388,2391,2397,2400,2403],{"className":2276},[607],[573,2278],{"className":2279,"style":2280},[611],"height:2.2514em;vertical-align:-0.93em;",[573,2282,2284,2287,2385],{"className":2283},[616],[573,2285],{"className":2286},[941,942],[573,2288,2290],{"className":2289},[881],[573,2291,2293,2377],{"className":2292},[665,666],[573,2294,2296,2374],{"className":2295},[670],[573,2297,2300,2355,2363],{"className":2298,"style":2299},[674],"height:1.3214em;",[573,2301,2302,2305],{"style":958},[573,2303],{"className":2304,"style":685},[684],[573,2306,2308],{"className":2307},[616],[573,2309,2311],{"className":2310},[616,661],[573,2312,2314,2347],{"className":2313},[665,666],[573,2315,2317,2344],{"className":2316},[670],[573,2318,2320,2332],{"className":2319,"style":675},[674],[573,2321,2323,2326],{"className":2322,"style":680},[679],[573,2324],{"className":2325,"style":685},[684],[573,2327,2329],{"className":2328,"style":689},[616],[573,2330,637],{"className":2331},[616],[573,2333,2334,2337],{"style":695},[573,2335],{"className":2336,"style":685},[684],[573,2338,2340],{"className":2339,"style":703},[702],[705,2341,2342],{"xmlns":707,"width":708,"height":709,"viewBox":710,"preserveAspectRatio":711},[713,2343],{"d":715},[573,2345,720],{"className":2346},[719],[573,2348,2350],{"className":2349},[670],[573,2351,2353],{"className":2352,"style":727},[674],[573,2354],{},[573,2356,2357,2360],{"style":1014},[573,2358],{"className":2359,"style":685},[684],[573,2361],{"className":2362,"style":1022},[1021],[573,2364,2365,2368],{"style":1025},[573,2366],{"className":2367,"style":685},[684],[573,2369,2371],{"className":2370},[616],[573,2372,2168],{"className":2373},[616],[573,2375,720],{"className":2376},[719],[573,2378,2380],{"className":2379},[670],[573,2381,2383],{"className":2382,"style":1044},[674],[573,2384],{},[573,2386],{"className":2387},[1050,942],[573,2389],{"className":2390,"style":1895},[733],[573,2392,2394],{"className":2393},[616,1899],[573,2395,1875],{"className":2396},[616],[573,2398],{"className":2399,"style":734},[733],[573,2401,879],{"className":2402},[738],[573,2404],{"className":2405,"style":734},[733],[573,2407,2409,2412,2415,2462,2465,2471,2474,2477],{"className":2408},[607],[573,2410],{"className":2411,"style":1796},[611],[573,2413,637],{"className":2414},[616],[573,2416,2418],{"className":2417},[616,661],[573,2419,2421,2454],{"className":2420},[665,666],[573,2422,2424,2451],{"className":2423},[670],[573,2425,2427,2439],{"className":2426,"style":1504},[674],[573,2428,2430,2433],{"className":2429,"style":680},[679],[573,2431],{"className":2432,"style":685},[684],[573,2434,2436],{"className":2435,"style":689},[616],[573,2437,637],{"className":2438},[616],[573,2440,2441,2444],{"style":1519},[573,2442],{"className":2443,"style":685},[684],[573,2445,2447],{"className":2446,"style":703},[702],[705,2448,2449],{"xmlns":707,"width":708,"height":709,"viewBox":710,"preserveAspectRatio":711},[713,2450],{"d":715},[573,2452,720],{"className":2453},[719],[573,2455,2457],{"className":2456},[670],[573,2458,2460],{"className":2459,"style":1539},[674],[573,2461],{},[573,2463],{"className":2464,"style":1895},[733],[573,2466,2468],{"className":2467},[616,1899],[573,2469,1875],{"className":2470},[616],[573,2472],{"className":2473,"style":734},[733],[573,2475,641],{"className":2476},[738],[573,2478],{"className":2479,"style":734},[733],[573,2481,2483,2486,2490,2496,2500,2503],{"className":2482},[607],[573,2484],{"className":2485,"style":748},[611],[573,2487,2489],{"className":2488},[616],"5",[573,2491,2493],{"className":2492},[616],[573,2494,760],{"className":2495},[759],[573,2497,2499],{"className":2498},[616],"20",[573,2501],{"className":2502,"style":1895},[733],[573,2504,2506],{"className":2505},[616,1899],[573,2507,1875],{"className":2508},[616],[559,2510,2512],{"id":2511},"typische-fehler","Typische Fehler",[2514,2515,2516,2770,2933],"ul",{},[2517,2518,1185,2519,2598,2599,2663,2664,2717,2718,2769],"li",{},[573,2520,2522,2539],{"className":2521},[576],[573,2523,2525],{"className":2524},[580],[582,2526,2527],{"xmlns":584},[586,2528,2529,2537],{},[589,2530,2531,2533],{},[592,2532,594],{},[632,2534,2535],{},[635,2536,791],{},[596,2538,794],{"encoding":598},[573,2540,2542],{"className":2541,"ariaHidden":603},[602],[573,2543,2545,2548,2551],{"className":2544},[607],[573,2546],{"className":2547,"style":657},[611],[573,2549,594],{"className":2550},[616,617],[573,2552,2554],{"className":2553},[616,661],[573,2555,2557,2590],{"className":2556},[665,666],[573,2558,2560,2587],{"className":2559},[670],[573,2561,2563,2575],{"className":2562,"style":675},[674],[573,2564,2566,2569],{"className":2565,"style":680},[679],[573,2567],{"className":2568,"style":685},[684],[573,2570,2572],{"className":2571,"style":689},[616],[573,2573,791],{"className":2574},[616],[573,2576,2577,2580],{"style":695},[573,2578],{"className":2579,"style":685},[684],[573,2581,2583],{"className":2582,"style":703},[702],[705,2584,2585],{"xmlns":707,"width":708,"height":709,"viewBox":710,"preserveAspectRatio":711},[713,2586],{"d":715},[573,2588,720],{"className":2589},[719],[573,2591,2593],{"className":2592},[670],[573,2594,2596],{"className":2595,"style":727},[674],[573,2597],{}," mit der Raumdiagonale verwechseln. Für ",[573,2600,2602,2624],{"className":2601},[576],[573,2603,2605],{"className":2604},[580],[582,2606,2607],{"xmlns":584},[586,2608,2609,2621],{},[589,2610,2611,2613,2615,2617,2619],{},[592,2612,594],{},[639,2614,879],{},[635,2616,1868],{},[1870,2618,1872],{},[1870,2620,1875],{},[596,2622,2623],{"encoding":598},"a = 4\\,\\text{cm}",[573,2625,2627,2645],{"className":2626,"ariaHidden":603},[602],[573,2628,2630,2633,2636,2639,2642],{"className":2629},[607],[573,2631],{"className":2632,"style":612},[611],[573,2634,594],{"className":2635},[616,617],[573,2637],{"className":2638,"style":734},[733],[573,2640,879],{"className":2641},[738],[573,2643],{"className":2644,"style":734},[733],[573,2646,2648,2651,2654,2657],{"className":2647},[607],[573,2649],{"className":2650,"style":1888},[611],[573,2652,1868],{"className":2653},[616],[573,2655],{"className":2656,"style":1895},[733],[573,2658,2660],{"className":2659},[616,1899],[573,2661,1875],{"className":2662},[616]," wäre das ",[573,2665,2667,2686],{"className":2666},[576],[573,2668,2670],{"className":2669},[580],[582,2671,2672],{"xmlns":584},[586,2673,2674,2683],{},[589,2675,2676,2679,2681],{},[635,2677,2678],{},"5,66",[1870,2680,1872],{},[1870,2682,1875],{},[596,2684,2685],{"encoding":598},"5{,}66\\,\\text{cm}",[573,2687,2689],{"className":2688,"ariaHidden":603},[602],[573,2690,2692,2695,2698,2704,2708,2711],{"className":2691},[607],[573,2693],{"className":2694,"style":748},[611],[573,2696,2489],{"className":2697},[616],[573,2699,2701],{"className":2700},[616],[573,2702,760],{"className":2703},[759],[573,2705,2707],{"className":2706},[616],"66",[573,2709],{"className":2710,"style":1895},[733],[573,2712,2714],{"className":2713},[616,1899],[573,2715,1875],{"className":2716},[616]," statt ",[573,2719,2721,2739],{"className":2720},[576],[573,2722,2724],{"className":2723},[580],[582,2725,2726],{"xmlns":584},[586,2727,2728,2736],{},[589,2729,2730,2732,2734],{},[635,2731,1948],{},[1870,2733,1872],{},[1870,2735,1875],{},[596,2737,2738],{"encoding":598},"6{,}93\\,\\text{cm}",[573,2740,2742],{"className":2741,"ariaHidden":603},[602],[573,2743,2745,2748,2751,2757,2760,2763],{"className":2744},[607],[573,2746],{"className":2747,"style":748},[611],[573,2749,2131],{"className":2750},[616],[573,2752,2754],{"className":2753},[616],[573,2755,760],{"className":2756},[759],[573,2758,2141],{"className":2759},[616],[573,2761],{"className":2762,"style":1895},[733],[573,2764,2766],{"className":2765},[616,1899],[573,2767,1875],{"className":2768},[616],".",[2517,2771,2772,2828,2829,2904,2905,2769],{},[573,2773,2775,2795],{"className":2774},[576],[573,2776,2778],{"className":2777},[580],[582,2779,2780],{"xmlns":584},[586,2781,2782,2792],{},[589,2783,2784,2786,2788,2790],{},[592,2785,885],{},[639,2787,879],{},[635,2789,637],{},[592,2791,594],{},[596,2793,2794],{"encoding":598},"d = 3a",[573,2796,2798,2816],{"className":2797,"ariaHidden":603},[602],[573,2799,2801,2804,2807,2810,2813],{"className":2800},[607],[573,2802],{"className":2803,"style":1320},[611],[573,2805,885],{"className":2806},[616,617],[573,2808],{"className":2809,"style":734},[733],[573,2811,879],{"className":2812},[738],[573,2814],{"className":2815,"style":734},[733],[573,2817,2819,2822,2825],{"className":2818},[607],[573,2820],{"className":2821,"style":1888},[611],[573,2823,637],{"className":2824},[616],[573,2826,594],{"className":2827},[616,617]," rechnen. Richtig ist der Faktor ",[573,2830,2832,2848],{"className":2831},[576],[573,2833,2835],{"className":2834},[580],[582,2836,2837],{"xmlns":584},[586,2838,2839,2845],{},[589,2840,2841],{},[632,2842,2843],{},[635,2844,637],{},[596,2846,2847],{"encoding":598},"\\sqrt{3}",[573,2849,2851],{"className":2850,"ariaHidden":603},[602],[573,2852,2854,2857],{"className":2853},[607],[573,2855],{"className":2856,"style":657},[611],[573,2858,2860],{"className":2859},[616,661],[573,2861,2863,2896],{"className":2862},[665,666],[573,2864,2866,2893],{"className":2865},[670],[573,2867,2869,2881],{"className":2868,"style":675},[674],[573,2870,2872,2875],{"className":2871,"style":680},[679],[573,2873],{"className":2874,"style":685},[684],[573,2876,2878],{"className":2877,"style":689},[616],[573,2879,637],{"className":2880},[616],[573,2882,2883,2886],{"style":695},[573,2884],{"className":2885,"style":685},[684],[573,2887,2889],{"className":2888,"style":703},[702],[705,2890,2891],{"xmlns":707,"width":708,"height":709,"viewBox":710,"preserveAspectRatio":711},[713,2892],{"d":715},[573,2894,720],{"className":2895},[719],[573,2897,2899],{"className":2898},[670],[573,2900,2902],{"className":2901,"style":727},[674],[573,2903],{},", nicht ",[573,2906,2908,2921],{"className":2907},[576],[573,2909,2911],{"className":2910},[580],[582,2912,2913],{"xmlns":584},[586,2914,2915,2919],{},[589,2916,2917],{},[635,2918,637],{},[596,2920,637],{"encoding":598},[573,2922,2924],{"className":2923,"ariaHidden":603},[602],[573,2925,2927,2930],{"className":2926},[607],[573,2928],{"className":2929,"style":1888},[611],[573,2931,637],{"className":2932},[616],[2517,2934,2935,2936,3010,3011,3085],{},"Beim Rückwärtsrechnen mit ",[573,2937,2939,2954],{"className":2938},[576],[573,2940,2942],{"className":2941},[580],[582,2943,2944],{"xmlns":584},[586,2945,2946,2952],{},[589,2947,2948],{},[632,2949,2950],{},[635,2951,637],{},[596,2953,2847],{"encoding":598},[573,2955,2957],{"className":2956,"ariaHidden":603},[602],[573,2958,2960,2963],{"className":2959},[607],[573,2961],{"className":2962,"style":657},[611],[573,2964,2966],{"className":2965},[616,661],[573,2967,2969,3002],{"className":2968},[665,666],[573,2970,2972,2999],{"className":2971},[670],[573,2973,2975,2987],{"className":2974,"style":675},[674],[573,2976,2978,2981],{"className":2977,"style":680},[679],[573,2979],{"className":2980,"style":685},[684],[573,2982,2984],{"className":2983,"style":689},[616],[573,2985,637],{"className":2986},[616],[573,2988,2989,2992],{"style":695},[573,2990],{"className":2991,"style":685},[684],[573,2993,2995],{"className":2994,"style":703},[702],[705,2996,2997],{"xmlns":707,"width":708,"height":709,"viewBox":710,"preserveAspectRatio":711},[713,2998],{"d":715},[573,3000,720],{"className":3001},[719],[573,3003,3005],{"className":3004},[670],[573,3006,3008],{"className":3007,"style":727},[674],[573,3009],{}," multiplizieren statt durch 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