In mathematics, a root is a number used to build up another number by repeated multiplication; in other words, one of the equal factors of a given number. For example, since 2 × 2 × 2 = 8, two is said to be the third root or cube root of eight. A root is written as a fractional power of a number. The square root of a number, x, is written as either √x or x 1/2, and represents a number that when multiplied by itself, gives the original number. The fourth root of x may be written in radical form as 4x or in power form as x 1/4. Of particular interest are √2, the square root of 2, and i, the square root of –1. (See also exponent; power.)


A root is also a solution of an equation; i.e. the value(s) of the variable for which the equation holds. For example, 3 is a root of the equation x 2 = 9. A root is also called a zero of a function because it is a value that will make the function zero (x = 3 will make the function f(x) = x 2 – 9 zero).


The word comes from the Indo-European werad, which originally meant the roots of a plant but was later generalized to mean the origins or beginnings of something, whether it was physical or mental.