This question already has an answer here:
- Proving $\sqrt 3$ is irrational. 10 answers
How do I solve this by prime factorization?
I came across a similar problem on MSE just recently, but I can't find it and I thoroughly searched for it. If anyone can find it, please post it in the comment so that I can delete this question.
Update: I don't know if it makes a difference, but please note that this is cubed root