Can someone help me to prove that: if q1 q2 is rational, then q1 and q2 is rational.

Can someone help me to prove that: if q1 q2 is rational, then q1 and q2 is rational.
I'd love to... however it's not the case.

12 is a rational number (Z is a subset of Q)

I can come up with infinite q1 and q2 to where q1*q2 = 12 but are not rational.

Here's one:

q1 = sqrt(72) q2 = sqrt(2)

You will notice that q1q2 is rational but neither q1 or q2 are rational.

Or did I misread the question?

Thank you kyop, I think the statement is false, I can only prove it in inverse statement.

Yes, the inverse is definitely true. That can easily be shown using the definition of rationals and the closure property.