So I was going through proof of irrationality of $\sqrt2$ and tried to construct a proof whether $\sqrt4$ is rational by proof of contradiction.
Proof: (By Contradiction)
For the purposes of contradiction assume $\sqrt4$ is irrational that means:
$\sqrt4$ can't be written in the form of $\frac{m}{n}$ where gcd(m,n) = 1
So $\sqrt4$ $\ne$ $\frac{m}{n}$
i.e 4 $\ne$ $\frac{m^2}{n^2}$
so 4*$n^2$ $\ne$ $m^2$
but then I am struck what to do? Please help me out.
P.S. I know we can easily write $\sqrt4$ as $\frac{2}{1}$ and that proves that it is rational but how would I go on proving by this approach.