prove or disprove if a number is irrational

Question

Prove or disprove :

I'm pretty sure this isn't true yet i can't find a counter example. Thanks in advance !

Answer 1

Sometimes when trying to prove/disprove an "if...then" statement, it's useful to quickly check if the contrapositive is any easier.

In this case, the contrapositive is:

If $x$ is rational, then $x^{1/3}$ is rational.

Is that true?

Answer 2

HINT: How about $x=2,3,4,5,6$?