How do I simplify $\sqrt {4(2- \sqrt{3})}$ into $\sqrt{6} - \sqrt{2}$ This might be a stupid question, but how do I get from $$\sqrt {4(2- \sqrt{3})}$$ to $$\sqrt{6} - \sqrt{2}$$ It is obvious if you squared both, they both equal $8 - 4 \sqrt{3}$, but I'm wondering how you can find the answer from the original expression.

Note that 
\begin{align}
4(2-\sqrt{3}) = 8 - 4\sqrt{3} = (\sqrt{6})^2 - 2\sqrt{6}\sqrt{2} + (\sqrt{2})^2
=
(\sqrt{6}-\sqrt{2})^2.
\end{align}
Therefore,
$$
\sqrt{6} -\sqrt{2} = \sqrt{4(2-\sqrt{3})}.
$$
