实数的运算 习题精选（一）
知识与技能
1．选择：
(1)下列各式是最简二次根式的是 ( )
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=39&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"39","h":"29","c":"a700384a769be3200909a0ec61456aa8.png"})
(2)在![](https://wkrtcs.bdimg.com/rtcs/image?w=445&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"445","h":"62","c":"7c574e8dd4b0271508c191fa3f16e42b.png"})
A．2个 B．3个 C．4个 D．5个
2．计算：
(1)![](https://wkrtcs.bdimg.com/rtcs/image?w=97&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"97","h":"34","c":"6f5829d61ce3aa5792bf996dad5acff0.png"})
(2)![](https://wkrtcs.bdimg.com/rtcs/image?w=133&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"133","h":"42","c":"1e55ab86903c3f894dcd48fb985bba31.png"})
(3)![](https://wkrtcs.bdimg.com/rtcs/image?w=110&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"110","h":"34","c":"f8f9252613847070a473567e4f6af8e7.png"})
(4)![](https://wkrtcs.bdimg.com/rtcs/image?w=99&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"99","h":"61","c":"b99c5d4eb59a8829579235d23bac676a.png"})
3．化简下列各式：
(1)![](https://wkrtcs.bdimg.com/rtcs/image?w=86&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"86","h":"29","c":"408291515538aaca34d726991d6eb0ff.png"})
(2)![](https://wkrtcs.bdimg.com/rtcs/image?w=112&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"112","h":"36","c":"3ccacf9518f652994f65096a45605f18.png"})
(3)![](https://wkrtcs.bdimg.com/rtcs/image?w=59&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"59","h":"29","c":"3bd99f02b6882e4c52b71f4f84c8d2e5.png"})
(4)![](https://wkrtcs.bdimg.com/rtcs/image?w=53&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"53","h":"54","c":"4f3ae2212f623087aeea216061d40e75.png"})
(5)![](https://wkrtcs.bdimg.com/rtcs/image?w=214&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"214","h":"29","c":"667752a6254aafa9c3cc9de2e76497a2.png"})
(6)![](https://wkrtcs.bdimg.com/rtcs/image?w=90&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"90","h":"54","c":"a6aa2fe6fd3364213a63e8a63d26eb23.png"})
4．化简下列各式：
(1)![](https://wkrtcs.bdimg.com/rtcs/image?w=64&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"64","h":"54","c":"e81db8e85c116b5033557c35298ae870.png"})
(2)![](https://wkrtcs.bdimg.com/rtcs/image?w=41&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"41","h":"54","c":"4e97881779e288a8bab64146de123a75.png"})
(3)![](https://wkrtcs.bdimg.com/rtcs/image?w=53&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"53","h":"54","c":"2c0311c409fbf3d0db52fe18f6097b1b.png"})
(4)![](https://wkrtcs.bdimg.com/rtcs/image?w=53&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"53","h":"54","c":"7628b08737d65856e40057ebd875a7a0.png"})
(5)![](https://wkrtcs.bdimg.com/rtcs/image?w=68&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"68","h":"29","c":"5bb2bb334a7d4de58c5e65c773cdf0a7.png"})
数学思考
最简二次根式要求被开方数是整数，且这个整数不含能开得尽方的因数．对于![](https://wkrtcs.bdimg.com/rtcs/image?w=34&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"34","h":"54","c":"21db3c3f0738b723ab76b23d5348aafa.png"})
(1)![](https://wkrtcs.bdimg.com/rtcs/image?w=116&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"116","h":"63","c":"844bc53fd1c31179e5cd72275c040ad8.png"})
(2)![](https://wkrtcs.bdimg.com/rtcs/image?w=144&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"144","h":"54","c":"c06cb32564dabd70f4f1d9895e560600.png"})
试着用上述的方法化简下列各式：![](https://wkrtcs.bdimg.com/rtcs/image?w=79&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"79","h":"54","c":"f2d239858ebade1da1de36857f368969.png"})
解决问题
物理学中的焦耳定律：![](https://wkrtcs.bdimg.com/rtcs/image?w=70&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"70","h":"25","c":"e8ac7ad18ac937c4a36fdeeb4fb783ab.png"})
开阔视野
实数范围内的因式分解
有些在有理数范围内不能分解的多项式，在实数范围内能继续分解．
如：![](https://wkrtcs.bdimg.com/rtcs/image?w=223&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"223","h":"29","c":"6294ea188364373e651fa0a7191e4225.png"})
在实数范围内分解下列因式：
(1)![](https://wkrtcs.bdimg.com/rtcs/image?w=55&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"55","h":"21","c":"26ec203c26e4e7918c145cd82ea4cf16.png"})
(2)![](https://wkrtcs.bdimg.com/rtcs/image?w=57&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"57","h":"21","c":"d9eb6c69529ad11b78f6368e7b8f1a7b.png"})
(3)![](https://wkrtcs.bdimg.com/rtcs/image?w=119&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"119","h":"29","c":"6117e5da461462b4993672f0c66c3649.png"})
(4)![](https://wkrtcs.bdimg.com/rtcs/image?w=187&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"187","h":"22","c":"d64b5d48ebcec8d8a0561c21392a58cf.png"})
(5)![](https://wkrtcs.bdimg.com/rtcs/image?w=91&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"91","h":"21","c":"9c3af1947e14e3e0babe9976594bd440.png"})
答案
知识与技能
1.（1）C（2）B
2.（1）0.02（2）4.41（3）－35(4) 12
3.(1)20 (2)![](https://wkrtcs.bdimg.com/rtcs/image?w=39&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"39","h":"29","c":"f0c8f465a85b4242f36ac4c80136bd0c.png"})
4.（1）![](https://wkrtcs.bdimg.com/rtcs/image?w=42&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"42","h":"43","c":"ea45bbccb43e2ebd85670f8c0f92e251.png"})
数学思考
（1）![](https://wkrtcs.bdimg.com/rtcs/image?w=121&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"121","h":"63","c":"fa557eeb192b02d610fc8d56a11dfba8.png"})
解决问题
![](https://wkrtcs.bdimg.com/rtcs/image?w=343&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"343","h":"26","c":"a5bb46212180a0d43c6308533a56f25c.png"})
开阔视野
（1）![](https://wkrtcs.bdimg.com/rtcs/image?w=156&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"156","h":"29","c":"22536b7b795e07cd9e77e0c49852d2a6.png"})
（2）![](https://wkrtcs.bdimg.com/rtcs/image?w=226&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"226","h":"29","c":"35678af4bf8869eca3eb026ce3a1529c.png"})
（3）![](https://wkrtcs.bdimg.com/rtcs/image?w=87&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"87","h":"34","c":"372b060ca4c729b98f8d12d75de0e141.png"})
（4）![](https://wkrtcs.bdimg.com/rtcs/image?w=226&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"226","h":"29","c":"5dbaedb504b79b61b7e1c7c29618e3a6.png"})
（5）![](https://wkrtcs.bdimg.com/rtcs/image?w=208&md5sum=f647663332114adb86181c88a68ea975&sign=c91c07110a&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=238&ipr={"t":"img","w":"208","h":"29","c":"83e640746cc0076d7077f92007c61096.png"})
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