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无理数平方根的计算
无理数平方根是难以确定的数,所以在加法和乘法的计算中,我们不能将其设为未知数(代数)。下面,我们要详细讲解代数式的计算。
【加法】
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0076_0001.jpg?sign=1739130564-FakkjlzeAgmfLt5jePYQ0aXsUHNEdXmf-0-e7e318f5efa61e11ea0d217c3bfc163a)
【减法】
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0076_0002.jpg?sign=1739130564-3o29IilIS1bHizb2GO3cWrpWd7r224uo-0-18668f92fd900c09ebeac094a504545b)
乘法和除法的计算过程更简单。
【乘法】
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0076_0003.jpg?sign=1739130564-99u8cCo6xvvSssnZBiF42NJuZaxTZYjv-0-b707a27d79a23d586820cbb26bca4089)
【除法】
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0076_0004.jpg?sign=1739130564-snKcgv0DvHFyvLlRdgfd53Fx5EFy3yIH-0-44a54fffa3bca28e8dd9545b168c4c84)
有些人可能会对无理数乘除法运算法则有疑问,我在此给大家分析一下。
现在,我们假设x是a的正平方根,y是b的正平方根。即,
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0076_0005.jpg?sign=1739130564-uOpORkPDjsARIAf2tMcmDtmatSfC2OS0-0-a7db560ef0a27d20e8efc4887b4dab42)
代入算式后,得出,
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0076_0006.jpg?sign=1739130564-wwqlMD2fCPEx9Az6cY2eqbycwyZc98sF-0-ec6be9a13f3e03d396be77287a84915e)
因此,
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0076_0007.jpg?sign=1739130564-u1O9oKTNXjc5r89SBZ8xH4TRJ1eFAceq-0-48a185b1650f3946dd8f428a4ff02069)
同上,除法只需将除法改成倒数的乘法计算即可。
包含2个以上的平方根的加减法,需要特别注意。
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0077_0001.jpg?sign=1739130564-EiKiCuqvfvgqnAKChEdv6XcASR2xfqv5-0-28b846f52f86e35a7f48356eaca33ada)
上面的算式是不成立的,你仔细一想,就会发现这样的计算是错误的。
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0077_0002.jpg?sign=1739130564-iVEodUH0I2zZIFj2qqEp58yldCTqt0JM-0-f5af3a916d8e3acf7857323f99917f83)
所以,
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0077_0003.jpg?sign=1739130564-mtmEa4LvAAlDQAJ2XY8uLsNaX44WsDoE-0-d9475c4cdfca9cb9cd309a86af92e4ca)
减法也一样,
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0077_0004.jpg?sign=1739130564-h2V5TNm71OTsRywyTSCf0xISkMFWCSw2-0-d3737acec558a87e7b8e2e80c12e259c)
结果很明显:
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0077_0005.jpg?sign=1739130564-t7niS83LJ07UXKoPa6SXmcOyr00X2LBG-0-8bc514ce7ec4d69266ba418a34e56668)