Two little hints:
a) Prove that if and then, would be rational (contradiction).
b) is countable and .
Try the rest.
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?