irrational to an irrational power can be rational

Let $A={\sqrt{2}}^{\sqrt{2}}$. If $A$ is a rational number, then it has the required property. If $A$ is an irrational number, let $B=A^{\sqrt{2}}$, then $B={\sqrt{2}}^2=2$ is a rational. Hence an irrational number to an irrational power can be a rational number. (In fact, it follows from the http://planetmath.org/node/3952Gelfond-Schneider Theorem that $A$ is transcendental, and therefore irrational.)

Title	irrational to an irrational power can be rational
Canonical name	IrrationalToAnIrrationalPowerCanBeRational
Date of creation	2013-03-22 13:42:35
Last modified on	2013-03-22 13:42:35
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	10
Author	Koro (127)
Entry type	Result
Classification	msc 11A99
Related topic	TechniquesInMathematicalProofs