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AoPS Wiki talk:Problem of the Day/July 12, 2011

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Problem

AoPSWiki: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.

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