计算
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211391dbaad6883061d2785b560ba1a5.png)
更新时间:2023-09-15 07:41:03
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【知识点】 运用平方差公式进行运算解读
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【推荐1】阅读下面的材料,解答后面给出的问题:
两个含有二次根式的代数式相乘,如果它们的积不含有二次根式,我们就说这两个代数式互为有理化因式,例如
与
,
与
.这样,化简一个分母含有二次根式的式子时,采用分子、分母同乘分母的有理化因式的方法就可以了,例如
,
.
(1)请你写出
的有理化因式:______________;
(2)请仿照上面给出的方法化简下列各式:
①
;
②
(
,
)
(3)已知
,
,求
的值.
两个含有二次根式的代数式相乘,如果它们的积不含有二次根式,我们就说这两个代数式互为有理化因式,例如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d012d124f04963fb72a68af40d5f8f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d012d124f04963fb72a68af40d5f8f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f190b17530d81d927c358ac84757a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34e01955f8c8fe2f0041b35d8d602a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0523291f5e05ffe80e41fa2c8311a0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d7a231c64e6d785b1e6a5824acd53f.png)
(1)请你写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/702f67c8a2d6c138032d41838a53d390.png)
(2)请仿照上面给出的方法化简下列各式:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89af06db29cad1f0d447d13cb929dfdc.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a43c353e2f2b5db993632cb44f84734.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/406185f4ad8bcd99e23adc8d289088ed.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61e60c71c305d45fd2856cea4e41d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db869ee52e295e5d93d008a52d2befb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d45ab196460f15608ed7a57cc7db0f10.png)
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