Gelfond-Schneider constant

The Gelfond-Schneider constant is

<math>2^\sqrt{2}=2.6651441...<math>

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

<math>\sqrt{2}^\sqrt{2}=1.6325269...<math>

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.