Rational numbers and Group Theory

["ADH"]

Hi,
I'm trying to solve this problem on group theory.  Most of the problems
I was able to handle were Zn and U(n) (integers under addition and
multiplication) but now I'm faced with rationals. I have no idea where
to start.
Problem: Let G= {a+b*sqrt(2)},where a and b are rational numbers not
both 0.  Prove that G is a group under ordinary multiplication.