1) Prove for any integer n, if n² is a multiple of 6 then so is n. To get credit, you should use the following facts in your proof:

If n² is even then so is n. (Proved)

If n² is a multiple of 3, then so is n. (Proved)

2)By contradiction, prove that the square root of 6 is irrational.

The result of part 1 should be be used as Lemma in your proof.