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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=1739130011-JmxLrLyBjJwhAPjS2PzytEwLBnirOk2Q-0-5c6955348249a8320f1e43b490974a75)
【减法】
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0076_0002.jpg?sign=1739130011-ITWnP9UYumiIhCUWwk2y6nJJl1zTNZdR-0-be7dee58acb9c20df3d365040b1a69a8)
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=1739130011-uHiJ5xovU3aI50Emf558OHV8CIIXw8h7-0-b3b350273be907d3a400e9a166ef3b99)
【除法】
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0076_0004.jpg?sign=1739130011-Gw29TkRDwQmCde8tUvq4qJdtcNDmISoF-0-e519e9988b30db1d93abe6d08f5a313a)
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=1739130011-opp523MWM1KdEtG0IOIAy7QH6pfz1obJ-0-1ee15ad4542bf56fd67d47375dd90929)
代入算式后,得出,
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0076_0006.jpg?sign=1739130011-DJ42j2TdoOo5N60oJ5H7hYaRRXCnAvHU-0-bdd5c9fcd44e0a968ca67ee003779d43)
因此,
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0076_0007.jpg?sign=1739130011-nRg9cJ4qn2NBy0Z8aX4LWK9ma3fzJSbU-0-03da57e08faa2eb7140fcef095fe0a90)
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=1739130011-zd2wBhox277D4iKx7nTa0Kf2lNi5gCzO-0-9ea1f0550b290a92f065dc53b6ad8bc6)
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=1739130011-bkMWwPWLyAOSNwIwH2UwXWgvcj4zXcgm-0-f9546ef4a34cecb432f36af505b8a396)
所以,
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0077_0003.jpg?sign=1739130011-LzY8fbr34YTyrExiJiI99aNcYANvZWVA-0-10aa1a7169cfc9fec7d3221ac56e2e59)
减法也一样,
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0077_0004.jpg?sign=1739130011-P7Vuf1zDu7zsLYqDeb6CTfHBVOpcaTrO-0-a6583b458d60ab11bdb9ea876248bd36)
结果很明显:
![](https://epubservercos.yuewen.com/E90007/11617807103194506/epubprivate/OEBPS/Images/figure_0077_0005.jpg?sign=1739130011-HWNeqDUMyLM9v6lSWMNnAGtFHBlS3NsF-0-fa13e772a55e7841ac095cc02306c01f)