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Arithmetic root

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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