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Difference between revisions of "Arithmetic root"

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''arithmetical value of the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013360/a0133602.png" />-th root of a real number <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013360/a0133603.png" />''
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''arithmetical value of the $n$-th root of a real number $a\geq0$''
  
A non-negative number the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013360/a0133604.png" />-th power of which is equal to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013360/a0133605.png" />. In considering the two real values of the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013360/a0133606.png" />-th root, where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013360/a0133607.png" /> 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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013360/a0133609.png" /> values of an <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013360/a01336010.png" />-th root, then one speaks of the values of the root in the domain of the complex numbers.
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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.

Latest revision as of 08:01, 12 April 2014

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://encyclopediaofmath.org/index.php?title=Arithmetic_root&oldid=19182