No. For example, is an irrational number, but is rational. However, any integer power of arationalnumber is rational.

You need to learn how to prove universal statement, implications and negations. In this case, you fix an arbitrary and assume that there exists a such that is irrational. Then you need to show that is not rational. You prove this by contradiction, i.e., you assume that is rational. Then is rational as well, contrary to the assumption.