The $n^{\text{th}}$ root of a number a expresses another number that, when multiplied by itself n times, will result in a. Aside from the radical symbol, the notation is made up of the radicand a and the index n. The resulting number is commonly called a radical. For example, the radical expression $\sqrt[4]{16}$ is the fourth root of 16. $\sqrt[4]{16}$ simplifies to 2 because 2 multiplied by itself 4 times equals 16. The general expression $\sqrt[n]{a}$ represents a number which equals a when multiplied by itself n times. For any real number a and natural number n, the expression $a^{\frac{1}{n}}$ is defined as the $n^{\text{th}}$ root of a. Note that a root with an even index is defined only for non-negative numbers. Therefore, if n is even, then a must be non-negative.

Just as with exponents, the most common roots have special names: square roots and cube roots have an index of 2 and 3, respectively.