Want to show: √12 is irrational

Since p is divisible by 3 and p²/q²=12, we can conclude that q is divisible by 2.

Since p is divisible by 3, we arrive at a contradiction since we assumed p to be prime. Therefore, the statement has been proven.

Since p is divisible by 3, we can write p=3n for some integer n. We should plug this value of p back into the equation p²=12q²