An n-th root of a number r is a number which, if n copies are multiplied together, makes r. It is also called a radical or a radical expression. It is a number k for which the following equation is true:
(for the meaning of , see Exponentiation.)
We write the nth root of r as . If n is 2, then the radical expression is a square root. If it is 3, it is a cube root. Other values of n are referred to using ordinal numbers, such as fourth root and tenth root.
For example, because . The 8 in that example is called the radicand, the 3 is called the index, and the check-shaped part is called the radical symbol or radical sign.
Roots and powers can be changed as shown in .
The product property of a radical expression is the statement that . The quotient property of a radical expression is the statement .
This is an example of how to simplify a radical.
If two radicals are the same, they can be combined. This is when both of the indexes and radicands are the same.