How can I prove that m, n in $m^2 = 6n^2$ are not integers?

Question

Having $n, m \neq 0 $ and $m^2 = 6n^2 $

How do I prove that $ n,m \notin \Bbb Z$ using somewhat formal methods?

Answer 1

Hint: Show that $m$ must be even. Then show that $n$ must be even.

Cancel and repeat.