Gelfond-Schneider constant

The Gelfond-Schneider constant is

$2^\sqrt{2}=2.6651441...$

which Aleksandr Gelfond proved to be a transcendental number using the Gelfond-Schneider theorem , answering one of the questions raised in Hilbert's seventh problem.

Its square root is

$\sqrt{2}^\sqrt{2}=1.6325269...$

which can be used in a nonconstructive proof that an irrational number to the power of an irrational number can sometimes produce a rational number.

See also

Gelfond's constant

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See also: Gelfond-Schneider constant, Gelfond's constant, Gelfond-Schneider theorem, Hilbert's seventh problem, Irrational number, Mathematics, Nonconstructive proof, Square root, Transcendental number