Suppose a*b=t (rational!)
a rational so a=p/q
t is rational so t=m/n
Hence, ab=m/n ==> b=m/n * q/p ==> b rational! A contradiction!
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 and and is rational, but is irrational, then is neccesarily irrational? Please provide a proof with your answer, thanks in advance.