Square root of a natural number to square root of another natural number

Question

Is there such integers $x,y$ which they're not perfect squares and they're not equal, such that:

$\sqrt{x}^\sqrt{y}$ is actually an integer? Or rational number?

Answer 1

By the Gelfond-Schneider Theorem, the number is always transcendental. In particular, it cannot be rational.

Answer 2

By Gelfond-Schneider theorem, you can show that $\sqrt{x}^\sqrt{y}$ is irrational.