# 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)