Prove that if $r^2$ is irrational then $r$ is irrational.

Question

Consider the statement

“For all real numbers $r$, if $r^2$ is irrational then r is irrational.”

Prove the statement by contraposition. Prove the statement by contradiction.

So I'm preparing for an exam in Discrete math, I came up across this question and can't seem to get the answer. I've tried using the formulas but I don't know how to get the answer.

Answer 1

Contraposition means you reverse the implication and negate both ends of it, so the sought result is that if $r$ is rational so is $r^2$, and this is trivial viz. $(a/b)^2=(a^2)/(b^2)$.