Prove that If a real number is irrational, then its square root is irrationa.

Learning Goal: I’m working on a discrete math question and need the explanation and answer to help me learn.

Prove the following statements using a proof by contraposition.

1 If a real number is irrational, then its square root is

irrational.

2 If r = mn, where m and n are positive integers, then

m

r or n

r.