阅读材料,回答问题: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:因为
,
,所以
与
,
与
互为有理化因式.
(1)
的有理化因式是______,
这样,化简一个分母含有二次根式的式子时,采用分子、分母同乘以分母的有理化因式的方法就可以了,例如:
,
;
(2)用上述方法对
进行分母有理化;
(3)利用所需知识判断:若
,
,则
,
的关系是______;
(4)计算:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9dfd557ae986d075449be3f30e45d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c35e58eaf847601c875f4597e910b5b0.png)
![](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)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c4f2557351db0241b4c018f7cd5bc3d.png)
这样,化简一个分母含有二次根式的式子时,采用分子、分母同乘以分母的有理化因式的方法就可以了,例如:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955d26dc64ba6622e6fa2a917727cf43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4930f014fedf2f3ecb4d4ddfd77b5091.png)
(2)用上述方法对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c005e5aa5fa88e8990cfe7e4bf86b6.png)
(3)利用所需知识判断:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c2c0a44c803d27cb14d4c4ba8caf69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff520d0942bbdf491ba049089d4d160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(4)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/001e63ec641114e623c1d9f34747b667.png)
更新时间:2023-09-07 20:05:12
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【推荐1】观察下列等式:
第一个等式:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f462bf7ae017e9d61905a4c9afe6047.png)
第二个等式:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f4478fb9b8ea9c24747ec60790f7eee.png)
第三个等式:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e480a52ed3afd61480e5e65b2bbfd2bd.png)
按上述规律,回答以下问题:
(1)请写出第四个等式:
;
(2)利用以上规律计算:
;
(3)求
的值.
第一个等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f462bf7ae017e9d61905a4c9afe6047.png)
第二个等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f4478fb9b8ea9c24747ec60790f7eee.png)
第三个等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e480a52ed3afd61480e5e65b2bbfd2bd.png)
按上述规律,回答以下问题:
(1)请写出第四个等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e4487468ab2823d6dbf7f0ebd2eb38.png)
(2)利用以上规律计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92d514d5ed4060c5923f6d25a7d8be7c.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/999ac9ea7bc5a61b3c0980817f1aacad.png)
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