$解:(2)猜想\sqrt{\frac{1}{8}(\frac{1}{9}-\frac{1}{10})}= \frac{1}{9}\sqrt{\frac{9}{80}}，$
$验证:\sqrt{\frac{1}{8}(\frac{1}{9}-\frac{1}{10})}$
$=\sqrt{\frac{1}{8×9×10}}$
$=\sqrt{\frac{9}{8×9²×10}}$
$=\frac{1}{9}\sqrt{\frac{9}{80}}.$
$(3)\sqrt{\frac{1}{n}(\frac{1}{n+1}-\frac {1}{n+2})}=\frac{1}{n+1}\sqrt{\frac{n+1}{n²+2n}}$
$验证:\sqrt{\frac{1}{n}(\frac{1}{n+1}-\frac {1}{n+2})}$
$=\sqrt{\frac{1}{n(n+1)(n+2)}}$
$=\sqrt{\frac{n+1}{n·(n+1)²·(n+2)}}$
$=\frac{1}{n+1}\sqrt{\frac{n+1}{n²+2n}}$
