<s>[INST] Square root of surds: $\sqrt{12+2\sqrt{6}}$? 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.
 [/INST] 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 $nm = 6$.
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