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?