Are these two fields equal

1. Apr 13, 2005

T-O7

Hey,
Does anyone know how to show that these fields are equal:
$$Q(\sqrt{p_1},\sqrt{p_2},...,\sqrt{p_k})=Q(\sqrt{p_1}+\sqrt{p_2}+...+\sqrt{p_k})$$,
where $$p_1,...,p_k$$ are distinct primes in Z.

One inclusion is clear to me, but i'm having problems showing they're equal. Thanks!

2. Apr 13, 2005

Hurkyl

Staff Emeritus
Induction on k, maybe?

3. Apr 13, 2005

T-O7

Right....note to self, always remember about induction. Thank you.
(although my solution using induction looks super messy)