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 x²+x-12=0, because (3)²+(3)-12=0 and (-4)²+(-4)-12=0. In the special case where f(x)=xⁿ-a for some number a, a root of f is called an nth root of a, denoted by <ROOT>n</ROOT><SQR>a</SQR> or a^1/n. For example, 2 is the third, or cube, root of 8 (<ROOT>3</ROOT><SQR>8</SQR>=2), since it satisfies the equation x³-8=0. Every number has n different (real or complex) nth 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 © 2007, Columbia University Press. All rights reserved.

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