:2019年春八下数学第十六章二次根式章末提升练习（新人教版）
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章末小结与提升
二次根式{■("概念" {■("二次根式" @"最简二次根式" )┤@"性质" {■("(" √a ")" ^2=a"(" a≥0")" @√(a^2 )="|" a"|" ={■(a"(" a≥0")" @▁(" -" a" " ) "(" a<0")" )┤ )┤@"运算" {■("乘法:" √a "•" √b=▁(" " √ab " " ) "(" a≥0"," b≥0")" @"除法:" √a/√b=√(a/b) "(" a≥0"," b>0")" @"加减法:合并被开方数相同的二次根式" )}"混合运算" )┤
类型1 非负数在二次根式中的应用
典例1 若x,y为实数,且√(3x"-" 1)+√(1"-" 3x)+y=4,则xy= .
【解析】根据二次根式的定义可知被开方数是非负数,于是{■(3x"-" 1≥0"," @1"-" 3x≥0"," )┤解得{■(x≥1/3 "," @x≤1/3 "," )┤即x=1/3,y=4,把x,y的值代入可得xy=1/3×4
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二次根式章末小结与提升
二次根式{■("概念" {■("二次根式" @"最简二次根式" )┤@"性质" {■("(" √a ")" ^2=a"(" a≥0")" @√(a^2 )="|" a"|" ={■(a"(" a≥0")" @▁(" -" a" " ) "(" a<0")" )┤ )┤@"运算" {■("乘法:" √a "•" √b=▁(" " √ab " " ) "(" a≥0"," b≥0")" @"除法:" √a/√b=√(a/b) "(" a≥0"," b>0")" @"加减法:合并被开方数相同的二次根式" )}"混合运算" )┤
类型1 非负数在二次根式中的应用
典例1 若x,y为实数,且√(3x"-" 1)+√(1"-" 3x)+y=4,则xy= .
【解析】根据二次根式的定义可知被开方数是非负数,于是{■(3x"-" 1≥0"," @1"-" 3x≥0"," )┤解得{■(x≥1/3 "," @x≤1/3 "," )┤即x=1/3,y=4,把x,y的值代入可得xy=1/3×4
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