# Arithmetic root

From Encyclopedia of Mathematics

*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.

**How to Cite This Entry:**

Arithmetic root.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Arithmetic_root&oldid=31593