Question

Prove that the square root of a positive integer is either an integer or an irrational number. I would like to prove the contrapositive.

Answer 1

see
http://math.stackexchange.com/questions/4467/sqrt-a-is-either-an-integer-or-an-irrational-number

Answer 2

I would actually not want to prove the contrapositive.
I would do two cases: assume a=b^2 for some integer b and assume a doesn't equal b^2 for some integer b.