There are many popular problems on irrational power rational. A very interesting read is this blog. And there are many specific examples where rational power irrational is rational (e.g. $2^{\log_2(3)}$). But what about $2^{\sqrt{2}}$? Is it rational or irrational?
2026-03-28 08:49:01.1774687741
Is $2^\sqrt{2}$ is rational or irrational?
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According to the Gelfond-Schneider theorem, it is transcendental (and, in particular, irrational).