Gelfond-Schneider Constant

The number $2^{\sqrt{2}}=2.66514414\ldots$ which is known to be Transcendental by Gelfond's Theorem.

References

Courant, R. and Robbins, H. What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, p. 107, 1996.