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pow:problem7s21

Problem 7 (due Monday, May 17)

Prove that the number $\left(\sqrt{13+\sqrt{52}}-\sqrt{13}\right)^{\mbox{ (\sqrt{14+\sqrt{52}}-\sqrt{13})^{ (\sqrt{15+\sqrt{52}}-\sqrt{13})}}}$ is irrational.

The problem was solved by Ashton Keith and John Mignone. For detailed solution see the following link Solution.