equivalence of theory of reals and Rationals

Question

https://math.stackexchange.com/questions/1520980/present-a-sentence-%CF%86-that-is-in-theory-of-reals-but-not-in-thoery-of-rationals

Following up from this question what is the approach to show that both the theories are equivalent

Th(R, 0, 1, +, ≤) equivalent to Th(Q, 0, 1, +, ≤)

Answer 1

One way to show that the theory of ordered divisible Abelian groups is complete is to prove that it is $\kappa$-categorical for some (and therefore all) uncountable $\kappa$.

This is not particularly difficult, since any model can be viewed as an ordered vector space over the rationals.