let $t$ be variable and let $k=\mathbb{C}(t)$ be the field of rational functions in t. let $f(x)=x^n-t$ for some positive integer $n$. let $\alpha$ be a root of $f$ in some field containing $\mathbb{C}(t)$. what is degree of $K(\alpha)$ over $K$
Now first of all we have to show $f(x)=x^n-t$ is irreducible. But how to show this as $f(x)$ is in $\mathbb{C}(t)[x]$, so the roots of $f(x)$ lies in $\mathbb{C}(t)[x]$. Then it is reducible. How to solve this problem, any help is appreciated thanks.