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

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{{:AoPSWiki:Problem of the Day/July 12, 2011}} | {{:AoPSWiki:Problem of the Day/July 12, 2011}} | ||

==Solution== | ==Solution== | ||

− | {{ | + | Note that |

+ | <cmath>\sqrt{1+\sqrt{1+\sqrt{1}}}=\sqrt{1+\sqrt{2}}</cmath> | ||

+ | Thus: | ||

+ | <cmath>(\sqrt{1+\sqrt{2}})^4=(1+\sqrt{2})^2=\boxed{3+2\sqrt{2}}</cmath> | ||

+ | and we are done. |