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Art of Problem Solving
AoPS Academy
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
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and language arts learners in grades 2-12.
![\[\sqrt{1+\sqrt{1+\sqrt{1}}}=\sqrt{1+\sqrt{2}}\]](http://latex.artofproblemsolving.com/d/3/8/d3899f78e2b0e50cab6a9ffb0dcfc16b7a78362c.png)
Thus:
![\[(\sqrt{1+\sqrt{2}})^4=(1+\sqrt{2})^2=\boxed{3+2\sqrt{2}}\]](http://latex.artofproblemsolving.com/0/1/5/0159ecc4d304098ff9ccffc061df0709172905c7.png)
and we are done.
Art of Problem Solving is an
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