Let R = {all real numbers}. Then <R,+> is a group. (+ is regular addition)

Let H = {a|a is an element of R and a^2 is rational}.

Is H closed with respect to the operation?

Is H closed with respect to the inverse?

Is H a subgroup of G?

I know what it means to be closed with respect to the operation and inverse but I'm not sure how to show it. Thanks.