Let $a_1$ and $a_2$ be positive integers and let $m = a_1 a_2$.
Prove that at least one of $a_1$ or $a_2$ is at least $\sqrt m$.
Disclosure:
This is for a homework question, though the question is using the product of three numbers and the cubed root. I am looking more for some direction on solving this then an answer, I am hoping by better understanding how this would work with the product of two numbers I can work out doing this with three.