# Difference between revisions of "AoPS Wiki talk:Problem of the Day/July 12, 2011"

## Solution

Note that $$\sqrt{1+\sqrt{1+\sqrt{1}}}=\sqrt{1+\sqrt{2}}$$ Thus: $$(\sqrt{1+\sqrt{2}})^4=(1+\sqrt{2})^2=\boxed{3+2\sqrt{2}}$$ and we are done.