【答案】
分析:(1)把原式中的被開(kāi)方數(shù)12變?yōu)?×4,27變?yōu)?×3,48變?yōu)?6×3,50變?yōu)?5×2,然后根據(jù)二次根式的乘法的逆運(yùn)算及化簡(jiǎn)公式
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/0.png)
=|a|進(jìn)行化簡(jiǎn),然后合并同類二次根式即可得到最簡(jiǎn)結(jié)果;
(2)利用乘法分配律給括號(hào)中每一項(xiàng)都乘以
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/1.png)
,利用二次根式的乘法法則及化簡(jiǎn)公式化簡(jiǎn)后,即可得到最后結(jié)果;
(3)根據(jù)運(yùn)算順序同級(jí)運(yùn)算從左到右依次計(jì)算,先算乘法運(yùn)算,系數(shù)相乘,并利用二次根式的乘法運(yùn)算進(jìn)行計(jì)算,然后把除法運(yùn)算化為乘法運(yùn)算,再利用乘法法則計(jì)算,最后根據(jù)化簡(jiǎn)公式
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/2.png)
=|a|進(jìn)行化簡(jiǎn),約分后即可得到最后結(jié)果;
(4)原式的第一項(xiàng)利用完全平方公式展開(kāi),第二項(xiàng)利用平方差公式化簡(jiǎn),去括號(hào)合并同類二次根式即可得到最后結(jié)果.
解答:解:(1)
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/3.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/4.png)
-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/5.png)
-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/6.png)
+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/7.png)
=2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/8.png)
-3
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/9.png)
-4
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/10.png)
+5
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/11.png)
=-5
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/12.png)
+5
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/13.png)
;
(2)
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/14.png)
=2
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/15.png)
×
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/16.png)
-3
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/17.png)
=12
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/18.png)
-3
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/19.png)
=9
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/20.png)
;
(3)
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/21.png)
=-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/22.png)
•
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/23.png)
•
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/24.png)
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/25.png)
=-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/26.png)
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/27.png)
=-a
2b
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/28.png)
;
(4)
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/29.png)
=9+12
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/30.png)
+20-(16-7)
=20+12
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131103202249149889486/SYS201311032022491498894018_DA/31.png)
.
點(diǎn)評(píng):此題考查了二次根式的混合運(yùn)算,二次根式的加減運(yùn)算實(shí)質(zhì)是合并同類二次根式,合并同類二次根式首先把所有項(xiàng)化為最簡(jiǎn)二次根式,找出被開(kāi)方數(shù)相同的項(xiàng)即為同類二次根式;二次根式的乘除運(yùn)算應(yīng)按照法則進(jìn)行計(jì)算,運(yùn)算的結(jié)果要化為最簡(jiǎn)二次根式.熟練掌握二次根式的乘除法運(yùn)算法則是解本題的關(guān)鍵.