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[sqr]
a or
a1/n. For example, 2 is the third, or cube, root of 8 ([root]3[sqr]8=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.
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