Hello everyone!

During my revision for my June exams (first year engineering) I came across this problem:

$\displaystyle

\frac{2\sqrt{2} + 2 \sqrt{6}}{\sqrt{2+\sqrt{3}}}

$

Simple math as it seems it kept me busy for 5 hours and stil no results. I know the answer is 4, but the catch is we are not allowed to use calculator. So I'm not interested in an answer, I'm interested in a method.

Any suggestions please?

I've already found multiple ways of simplifying it, so that there is no division by a square root but the method is still eluding me...