# How to simplify $\frac{4 + 2\sqrt6}{\sqrt{5 + 2\sqrt{6}}}$?

I was tackling through an olympiad practice book when I saw one of these problems:

If $x = 5 + 2\sqrt6$, evaluate $\Large{x \ - \ 1 \over\sqrt{x}}$?

The answer written is $2\sqrt2$, but I can't figure my way out through the manipulations. I just know that I have the following:$${4+ 2\sqrt6} \over {\sqrt{5 + 2\sqrt6}}$$

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My next step would be multiplying by the conjugate: $\frac {\sqrt{ 5-2\sqrt 6}}{\sqrt {5-2\sqrt 6}}$. – Ross Millikan Dec 3 '12 at 14:54

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