# Evaluating a (probably) arithmetic progression

Recently, I've stumbled upon an equation (9th grade) that I know nothing about. It looks like this:

$${\frac {1} {\sqrt {5}+ \sqrt {2}}}+{\frac {1} {\sqrt {8}+ \sqrt {5}}} +{\frac {1} {\sqrt {11}+ \sqrt {8}}}+...+{\frac {1} {\sqrt {38}+ \sqrt {35}}}$$

Obviously, if you continue by replacing three dots, you'll get:

$${\frac {1} {\sqrt {14}+ \sqrt {11}}} + {\frac {1} {\sqrt {17}+ \sqrt {14}}}$$ so on, so on until last.

But what am I supposed to do to solve this? Roughly translating from my language the task looks like: Evaluate the sum.

I mean, it doesn't look like arithmetic progression, because I am not able to find d or geometric progression to find q, so what should I do to solve it?

Hint: square roots in denominators are usually not nice to work with. So get rid of them: Expand the first fraction by $$\sqrt5-\sqrt2$$, the second fraction by $$\sqrt8-\sqrt5$$, and so on. Then add them together.