第144页 - 亮点给力提优课时作业本八年级数学江苏版

4

$7+4\sqrt {2}$

$=2\sqrt {3}-8\sqrt {3}+\sqrt {3}$

$=-5\sqrt {3}$

$=6\sqrt {3}+\frac {\sqrt {2}}{2}+\frac {3}{5}-4\sqrt {2}$

$=\frac {31\sqrt {3}}{5}-\frac {7\sqrt {2}}{2} $

$=2\sqrt {2}+3×\frac {\sqrt {3}}{3}-\frac {\sqrt 2}{2}+\frac {\sqrt 3}{2}$

$=\frac {3\sqrt 2}{2}+\frac {3\sqrt {3}}{2}$

$=4b · \frac {\sqrt {ab}}{b}+\frac {2}{a} · a \sqrt {ab}-3a · \frac {\sqrt {ab}}{a}- 3 \sqrt {ab}$

$=4 \sqrt {ab}+2 \sqrt {ab}-3 \sqrt {ab}-3 \sqrt {ab}$

$=0$

解：原式$=6 \sqrt {xy}+3 \sqrt {xy}-4 \sqrt {xy}-6 \sqrt {xy}= - \sqrt {xy}$

当$x=\frac {3}{2}$，$y=27$时，原式$=- \sqrt {\frac {3}{2}×27}=- \sqrt {\frac {81}{2}}=-\frac {9\sqrt {2}}{2}$

D

-9≤m≤25

解：$(1)\frac {\sqrt {5}-1}{2}-\frac {2}{\sqrt 5-1}= \frac {\sqrt {5}-1}{2}-\frac {\sqrt {5}+1}{2}=-1$；

$ \frac {\sqrt {8}-2}{2}-\frac {2}{\sqrt 8-2}= \frac {\sqrt {8}-2}{2}-\frac {\sqrt {8}+2}{2}=-2$；

$ \frac {\sqrt {13}-3}{2}-\frac {2}{\sqrt {13}-3}= \frac {\sqrt {13}-3}{2}-\frac {\sqrt {13}+3}{2}=-3$；

$ \frac {\sqrt {20}-4}{2}-\frac {2}{\sqrt {20}-4}=\frac {\sqrt {20}-4}{2}-\frac {\sqrt {20}+4}{2}=-4$

$(2)$第$5$个式子为$\frac {\sqrt {29}-5}{2}-\frac {2}{\sqrt {29}-5}$，其结果为$-5$

$(3)$第$n$个式子为$\frac {\sqrt {n²+4}-n}{2}-\frac {2}{\sqrt {n^2+4}-n}$，其结果为$-n$，证明如下：

$\frac {\sqrt {n²+4}-n}{2}-\frac {2}{\sqrt {n^2+4}-n}=\frac {\sqrt {n²+4}-n}{2}-\frac {\sqrt {n^2+4}+n}2=-n$