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I know the famous proof that uses $x={\sqrt{2}}^{\sqrt{2}}$ to prove that there must exist an irrational to an irrational power that evaluates to a rational. But I don't know if $x$ itself is known to be irrational or rational.

Could someone enlighten me? Thanks!

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marked as duplicate by Najib Idrissi, Claude Leibovici, Siminore, Alex M., TravisJ Sep 16 '15 at 13:03

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It's transcendental by the Gelfond-Schneider theorem.

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