How to sum $\sum _{n=0}^{120}\:\frac{1}{\sqrt{n+1}+\sqrt{n}}\:$ without the use of a calculator? I'm learning about series and a textbook gives me the problem:
$\sum _{n=0}^{120}\:\frac{1}{\sqrt{n+1}+\sqrt{n}}\:$
But I can't figure out how to solve it, what process to follow or formula to use.  I just know it diverges if it goes to infinity.
Also is it possible to compute the result without the use of a calculator (just by hand)?
Tell me if there is any english issues in the post, I am still learning the language

HINT
Notice that
\begin{align*}
\frac{1}{\sqrt{n+1} + \sqrt{n}} = \frac{1}{\sqrt{n+1} + \sqrt{n}}\times\frac{\sqrt{n+1} - \sqrt{n}}{\sqrt{n+1} - \sqrt{n}} = \sqrt{n+1} - \sqrt{n} 
\end{align*}
