Let $\displaystyle B = \left\{ \sqrt{x} \; | \; x = 1\text{ or } x\text{ is prime}\right\},\; S = \left\{ \sum_{k=1}^n a_k b_k \;|\; n\in N, \;a_k \in Q,\; b_k \in B \right\}$

Prove that $\displaystyle S$ is a linear space over $\displaystyle Q$ with a basis $\displaystyle B$