Possible Duplicate:
The square roots of the primes are linearly independent over the field of rationals
I would like to prove that the family $\{\sqrt{p}, p\text{ prime number} \}$ is linearly independent in $\mathbb R$ where $\mathbb R$ is a $\mathbb Q$-vector space.
I know how to prove this for up to 4 elements but I would like a general proof as elementary as possible.
Thanks in advance.
Sebastian