root (mathematics)

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 n th root of a, denoted by na or a^1/n . For example, 2 is the third, or cube, root of 8 ( 3 8 =2), since it satisfies the equation x³ -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.

root In mathematics, fractional power of a number. The square root of a number, x, is written as either √x or x½. The fourth root of x may be written in radical form as ⁴√x or in power form as x√. The fourth root of 16, for example, is 2 since 2 × 2 × 2 × 2 = 16.