【答案】
分析:(1)根據(jù)二次根式的混合運(yùn)算法則和順序計(jì)算即可;
(2)根據(jù)積的乘方公式的逆運(yùn)算公式a
n•b
n=(ab)
n計(jì)算即可;
(3)先把條件a和代數(shù)式化簡(jiǎn),再把化簡(jiǎn)后的a值代入化簡(jiǎn)后的代數(shù)式求值即可.
解答:解:(1)原式=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/0.png)
+4
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/1.png)
,
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/2.png)
+4
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/3.png)
,
=5
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/4.png)
;
(2)原式=[(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/5.png)
+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/6.png)
)(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/7.png)
-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/8.png)
)]
10(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/9.png)
-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/10.png)
)
2,
=110×(5-2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/11.png)
),
=5-2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/12.png)
;
(3)∵
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/13.png)
=2-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/14.png)
,
∴
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/15.png)
=a-1-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/16.png)
又∵a-2=-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/17.png)
<0,
∴原式=a-1-(2-a)=2a-3
=4-2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/18.png)
-3,
=1-2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103200403819129458/SYS201311032004038191294016_DA/19.png)
.
點(diǎn)評(píng):(1)本題考查了二次根式的混合運(yùn)算:二次根式乘法、除法及加減法運(yùn)算法則的綜合運(yùn)用.學(xué)習(xí)二次根式的混合運(yùn)算應(yīng)注意以下幾點(diǎn):①與有理數(shù)的混合運(yùn)算一致,運(yùn)算順序先乘方再乘除,最后加減,有括號(hào)的先算括號(hào)里面的;
(2)本題考查了積的乘方公式的逆運(yùn)算公式a
n•b
n=(ab)
n在二次根式計(jì)算里面的運(yùn)用;對(duì)有理數(shù)實(shí)用的公式對(duì)無理數(shù)照樣實(shí)用;
(3)本題考查了二次根式的化簡(jiǎn)求值,在化簡(jiǎn)求值時(shí)一定要先化簡(jiǎn)再代入求值;二次根式運(yùn)算的最后,注意結(jié)果要化到最簡(jiǎn)二次根式,二次根式的乘除運(yùn)算要與加減運(yùn)算區(qū)分,避免互相干擾.