Answer:
It is irrational.
Step-by-step explanation: And it is not the solution to any polynomial equation with integer coefficients, so it is also transcendental.
However, it IS possible to raise an irrational number to an irrational power and get a rational number.
For example, let x=2–√. It is well known that this is irrational.
Let y=2log25. This is irrational, since log25 is irrational.
But xy=2–√(2log25)
=2(log25)=5.
This last equation is true because logs are inverses of powers. For example, 2(log2n)=n.
I would have thought any irrational raised to an irrational was always irrational, until I saw an example like this.
It is still a surprising result to me.