Root, in arithmetic, is a quantity that yields a given quantity when it is taken as a factor a specified number of times (see Factor ). The number of times the root is taken as a factor is called its index. Roots are named from their indexes. Thus, 3 is a fourth root of 81, because 3 X 3 X 3 X 3 = 81. Roots with indexes of 2 and 3 are also called square roots and cube roots, respectively.
A root in algebra is a solution of an equation–that is, it is a quantity which, when substituted for the variable in an equation, satisfies the equation. For example, 3 is a root of x + 2 = 5, because if 3 is substituted for the variable x, the equation correctly reads 3 + 2 = 5. See also Algebra ; Cube root ; Square root .
