# Simple Field Extension Question

1. Apr 2, 2009

### jeffreydk

I'm currently trying to prove that (for a field extension $K$ of the field $F$) if $u\in K$ and $u^2$ is algebraic over $F$ then $u$ is algebraic over $K$.

I thought of trying to prove it as contrapositive but that got me nowhere--it seems so simple but I don't know what to use for this. Any help with this would be greatly appreciated.

2. Apr 2, 2009

### eok20

Well clearly u is algebraic over K (it is an elemnt of K) so I'm guessing you mean to say that u is algebraic over F. Well if u^2 is algebraic over F then let f be a polynomial in F[x] such that f(u^2)=0. I don't want to give it away but if you think about the polynomial f(x^2)...

3. Apr 2, 2009

### jeffreydk

Oh wow yea, ok it's pretty clear. I think I was complicating things. Thanks.