Check when the series $\sum ( \sqrt{n+1}-\sqrt{n})^ a$, $a\in \Bbb{R}$ converges.

$Attempt$: Let us focus on $a\_n= ( \sqrt{n+1}-\sqrt{n})^ a$. $a\_n=( \sqrt{n+1}-\sqrt{n})^ a=( (\sqrt{n+1}-\sqrt{n})\cdot{\sqrt{n+1}+\sqrt{n}\over \sqrt{n+1}+\sqrt{n}})^ a=({1\over \sqrt{n+1}+\sqrt{n}})^a$. 

I know I sort of have to find an $a$ for which $({1\over \sqrt{n+1}+\sqrt{n}})^a\le {1\over n^b}$ where $b>1$. Any suggestion for a way to $resume$ my attempt? Thank you.