The definition is: $E$ is a simple radical extension of $F$, if there exists some integer $n$, such that $E=F(a)$, where $a^n\in F$.
Question: let $d$ be the degree $d=[E:F]$, then we can only claim $n\ge d$, rather than $n=d$?
My work: for example, let $\omega=e^{i2\pi/3}$, $F=Q, E=Q(\omega)$, the irreducible polynomial for $\omega$ is $\omega^2+\omega+1=0$, hence $d=[E:F]=2$. While $\omega^3=1\in Q$, hence $n=3$,
$$n=3\ge2=d$$