Irrational Raised to Irrational

[nycmath]

Precalculus
David Cohen
Edition 3
Chapter 1, Section 1.1

66. Can an Irrational number raised to an irrational power yield an answer that is rational?

(a) Let A = (1/2)^(1/2)

Now, either A is rational or A is irrational. If A is rational, we are done. Why?

(b) If A is irrational, we are done. Why?

Hint: Consider A^(1/2)