# root

**root,**in mathematics, number or quantity

*r*for which an equation

*f*(

*r*)=0 holds true, where

*f*is some function. If

*f*is a polynomial,

*r*is called a root of

*f;*for example,

*r*=3 and

*r*=−4 are roots of the equation

*x*

^{2}+

*x*−12=0, because (3)

^{2}+(3)−12=0 and (−4)

^{2}+(−4)−12=0. In the special case where

*f*(

*x*)=

*x*

^{n}−

*a*for some number

*a,*a root of

*f*is called an

*n*th root of

*a,*denoted by

*n*

*a*

*a*

^{1/n}. For example, 2 is the third, or cube, root of 8 (

*x*

^{3}−8=0. Every number has

*n*different (real or complex)

*n*th roots; e.g., there are two square roots of 9 (3 and −3) since (3)(3)=9 and (−3)(−3)=9.

*The Columbia Electronic Encyclopedia,* 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

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