最简二次根式最简二次根式满足下列条件的二次根式,叫做最简二次根式。(1)被开方数中的因数是整数,因式是整式;(2)被开方数中不含能开得尽方的因数或因式;(3)分母中不含根号。最简二次根式的定义最简二次根式的定义判断下列各式是否为最简二次根式?12ba245952mmx3021143xyx2422525mm(5)();(2)();(3)();(4)();(1)();(6)();(7)();√×××××√辨析训练辨析训练1、把下列各式化成最简二次根式:练习2245593535abababab3322222ababababab2236333332162162423320,0ababba2450a23321、2、3、4、2、计算(1)(2)27104521215解(1):方法1:303331027102710230333102710方法2:解(2):方法1:4523532154545245121545212152215452153215方法2:15535532321545212153、已知:,如何求与的近似值?(结果保留两位有效数字)414.1221882121解:22212414.171.0707.022414.12828.28.222例2把下列各式化成最简二次根式:(1);(2)3xyx2114解(1)21143x>0,y0yxx23423422234264623xyxxxyxxxxyxxy(2)把下列各式化成最简二次根式:(1)(2)(3)(4)8.02142200,0,0ababcc23108xxx19933232422222222225204525abcababcabcccccc222233241122228824416xxxxxxxxxxxxx练习二44225250.8555555把下列各式化成最简二次根式:(1)(2)(3)(4)448242252250mmm01.004.0321112aaaaaa强化训练强化训练2844641616545422222522525959mmmmmm550.040.010.05100102322111111211111111aaaaaaaaaaaaaaaaaaaaaaaaaa1.最简二次根式的概念.满足下列条件的二次根式,叫做最简二次根式。(1)被开方数中的因数是整数,因式是整式;(2)被开方数中不含能开得尽方的因数或因式;(3)分母中不含根号。2.如何化二次根式为最简二次根式.课堂小结:课堂小结: