So, this is a question in my textbook. I'm sure it's a very simple answer, that's right under my nose, but that I'm just missing for some reason. Anyway, if we have two numbers $\displaystyle a$ and $\displaystyle b$ and $\displaystyle a$ is rational, but $\displaystyle b$ is irrational, then is $\displaystyle ab$ neccesarily irrational? Please provide a proof with your answer, thanks in advance.