题目内容
下面说法中,错误的是( )A.当x<0时,根式
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_ST/0.png)
B.
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_ST/1.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_ST/2.png)
C.当x<-2时,
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_ST/3.png)
D.
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_ST/4.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_ST/5.png)
【答案】分析:根据二次根式有意义的条件,分母有理化以及二次根式的性质对各选项分析判断后利用排除法求解.
解答:解:A、当x<0时,根式
在实数范围内有意义,正确,故本选项错误;
B、∵
=
=
+1,∴
分母有理化的结果是
+1,正确,故本选项错误;
C、当x<-2时,x+1<0,
=-x-1,正确,故本选项错误;
D、∵![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/7.png)
=
b
,6b
=6b×
=3
,
∴![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/14.png)
与6b
是同类二次根式,故本选项正确.
故选D.
点评:本题考查了最简二次根式,二次根式有意义的条件,二次根式的性质,以及分母有理化,是基础题,准确计算是解题的关键.
解答:解:A、当x<0时,根式
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/0.png)
B、∵
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/1.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/2.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/3.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/4.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/5.png)
C、当x<-2时,x+1<0,
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/6.png)
D、∵
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/7.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/8.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/9.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/10.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/11.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/12.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/13.png)
∴
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/14.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/15.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103202841877879213/SYS201311032028418778792012_DA/16.png)
故选D.
点评:本题考查了最简二次根式,二次根式有意义的条件,二次根式的性质,以及分母有理化,是基础题,准确计算是解题的关键.
![](http://thumb2018.1010pic.com/images/loading.gif)
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