Want to show: √12 is irrational

Since we have concluded that p and q are both divisible by 3, we contradict the fact that p and q are coprime. So p and q cannot exist, and therefore √12 is irrational

We now know that q is divisible by 3, so we can write q=3m for some integer m. Then plug this back into 12 = ^p⁄_q where p=3n. Now repeat the same process with m and n.