Is u Algebraic Over K if u^2 is Algebraic Over F?

[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.

 

[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)...

 

[jeffreydk]

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