Quadratic field extension of the rational number

about the set of number W={a+(2^(1/2))b: a,b∈Q}
Q is set of rational number.

a)how to show x=a+(2^(1/2))b∈Q if and only if b=0?
b)how to show W is countable?
c)how to show that between any two distinct real number is an element of W?
d)how to show W is an ordered field?

Two little hints:

a) Prove that if and then, would be rational (contradiction).

b) is countable and .

Try the rest.