Rationalizing the denominator of $\frac{2}{\sqrt{2+\sqrt{2+\sqrt{2}}}}$ 
Simplify 
  $$\frac{2}{\sqrt{2+\sqrt{2+\sqrt{2}}}}$$

I think this should be expressed without square roots at the denominator. I tried to multiply by conjugate.

I used conjugates twice, got
$$ \sqrt 2 \cdot  \sqrt{2 + \sqrt 2} \cdot \sqrt{2 - \sqrt{2 + \sqrt 2}} $$
Perhaps these can be multiplied together to make something nice. I don't know. Note that no information about the source of the question is given. 
