<s>[INST] Evaluate this square root $\sqrt{6 + 2\sqrt{5}} + \sqrt{6 - 2\sqrt{5}}$ 
I have no clue where to begin. I would appreciate a hint, the answer should be
$2\sqrt{5}$
In general, how do you evaluate 
$\sqrt{a + b} + \sqrt{a - b}$?
Thanks!
 [/INST] Notice that $(\sqrt{5}-1)^2 = 6-2\sqrt{5}$ and $(\sqrt{5}+1)^2 = 6+2\sqrt{5}$, hence:
$$ \sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}=(\sqrt{5}+1)+(\sqrt{5}-1)=2\sqrt{5}. $$
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