Arithmetic Root

arithmetical value of the $n$-th root of a real number $a\geq0$

A non-negative number the $n$-th power of which is equal to $a$. In considering the two real values of the $n$-th root, where $n$ is an even number, of a non-negative number, one speaks of the algebraic values of the root in the domain of the real numbers; if, on the other hand, one is considering all $n$ values of an $n$-th root, then one speaks of the values of the root in the domain of the complex numbers.