Discrete Math: Proofs

Use a form of Direct Proof to prove that any non-zero rational number can be written as the product of 2 irrational numbers. A partial proof has been given below.

1. Let 𝑛 be any non-zero rational number.
2. Then, 𝑛 can be written as √2 ( n / √2 )
3. √2 is an irrational number.

So what are your thoughts on this? You've been given virtually all the pieces in the partial solution

I know how to solve this by contradiction, but I'm not too sure how to go about using direct proofs.
I guess to start we need to prove that ( n / √2 ) is irrational as well, and that translates to a / b(√2 )
I'm not sure how to carry on from here