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.