Proof by contradiction is almost never necessary. Proof that if a number has a rational number square root, it must be a square: Let's suppose that sqrt(p

Proof by contradiction is almost never necessary. Proof that if a number has a rational number square root, it must be a square: Let's suppose that sqrt(p) = a/b That means that p = (a^2)/(b^2) That means that p * b^2 = a^2 Therefore p is a square (by counting prime factors).