Question:
For irrational numbers x,y show that x^y is not necessarily irrational.
How would I go about this question? I thought about proof by contradiction but don't think it will work because x^y could also be irrational. Do I just find a counter-example?
Statement : For irrational numbers x,y show that x^y is not necessarily irrational.
This statement is equivalent to disproving the statement : For irrational numbers x,y show that x^y is necessarily irrational.
Therefore, one counter-example (such as the one given by Drexel) is enough to disprove the latter, and thus to prove the original statement.