real analysis - Limit exercise from Rudin: $limlimits_{n to infty} sqrt{n^2+n} -n$

This is Chapter 3, Exercise 2 of Rudin's Principles.

Calculate $\lim\limits_{n \to \infty} \sqrt{n^2+n} -n$.

Hints will be appreciated.

Answer

Hint:

$$\frac{\sqrt{n^2+n}-n}{1} = \frac{\sqrt{n^2+n}-\sqrt{n^2}}{1}\times \frac{\sqrt{n^2+n}+\sqrt{n^2}}{\sqrt{n^2+n}+\sqrt{n^2}} = \cdots$$
I will expand more if needed.