第37页

信息发布者：
B
$\sqrt{x^2+4x+8} $
5
$\sqrt{13}+3$
$解:(2)原式=\frac {\sqrt n-\sqrt {n-2}}{(\sqrt n+\sqrt {n-2})(\sqrt n-\sqrt {n-2})}$
$\hspace{1.85cm}=\frac {\sqrt n-\sqrt {n-2}}{2}.$
$ (3)原式=\frac{1}{3}(\sqrt{5}-\sqrt{2}+\sqrt{8}-\sqrt{5}+\sqrt{11}-\sqrt{8}+···+\sqrt{3n+2}-\sqrt{3n-1})(\sqrt{3n+2}+\sqrt 2) $
$\hspace{1.25cm}=\frac{1}{3}(\sqrt{3n+2}-\sqrt{2})(\sqrt{3n+2}+\sqrt 2) $
$\hspace{1.25cm}=\frac{1}{3}\left[(\sqrt{3n+2})^2-(\sqrt{2})^2\right]$
$\hspace{1.25cm}=\frac{1}{3}(3n+2-2)$
$\hspace{1.25cm}=n. $
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