Originally Posted by

**mulaosmanovicben** Prove that

$\displaystyle \mathbb{Q}$($\displaystyle \sqrt{2}$,$\displaystyle \sqrt{3}$) is isomorphic to $\displaystyle \mathbb{Q}$($\displaystyle \sqrt{2}$ + $\displaystyle \sqrt{3}$)

ATTEMPT:

Well we have been learning about extension fields. I know that if F is a field and a is a zero of a polynomial p(x) in F[x] then F(a) is isomorphic to F[x]/<p(x)>. So if i can find a polynomial such that $\displaystyle \sqrt{2}$,$\displaystyle \sqrt{3}$ and $\displaystyle \sqrt{2}$ + $\displaystyle \sqrt{3}$ are all zero that would be great.

I really have no idea what to do can you guys give me hints?