Square root of surds: $\sqrt{12+2\sqrt{6}}$?

Question

I got this question

Find the square root of $12+2\sqrt{6}$ expressing your answer in the form $\sqrt{m}+\sqrt{n}$.

I have no idea what this means and how to go about it.

Answer 1

Let $x = \sqrt{12 + 2\sqrt{6}} = \sqrt{n} + \sqrt{m}$. Then $x^2 = 12 + 2\sqrt 6 = n + m + 2 \sqrt{nm}$.

Find $n$ and $m$ such that $n + m = 12$ and $nm = 6$.