I saw that questions about this have been posted before, but I don't want to spoil things for myself by prematurely looking up an answer. I just want to know if this proof I came up with is valid:
"Suppose $\sqrt 3$ is rational. Then $\sqrt 3 = \frac p q$, where $p,q$ are integers and $q \ne 0$. But then that means $q\sqrt 3 = p$, and we know that no integers satisfy this, so $\sqrt 3$ must be irrational."
Is this good? If not, why not?