# root

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 ^{4}√*x* 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.