Element expressible by radicals

An element $\alpha$ of a field $L$ is expressible by radicals over a subfield $K\subseteq L$ if it can be obtained from elements of $K$ by finitely many additions, substractions, multiplications, divisions, and taking $n$-th roots.

More formally, $\alpha$ is expressible by real radicals if there exists a tower of extensions :

$$K = E_0 \subset \ldots \subset E_n$$

where $\alpha$ is in $E_n$ and, for each $i$, $E_i\subset E_{i+1}$ is an elementary radical extension.

Remarks

• One says expressible by real radicals if the tower of extensions is entirely included in $\mathbb{R}$.