For any real number a, an nth root of a is a number x such that xⁿ = a. When n =  2, it is called a square root, and when n =  3 a cube root.

First consider n even. If a<0, there is no real number x such that xⁿ = a. If a > 0, there are two such numbers, one positive and one negative. For a≥0, the notation $\sqrt[n]{a}$ is used to denote quite specifically the non-negative nth root of a. For example, $\sqrt[4]{16}\text{=}2$, and 16 has two real fourth roots, namely 2 and −2.

Next consider n odd. For all values of a, there is a unique number x such that xⁿ = a, and it is denoted by an $\sqrt[n]{a}$. For example, $\sqrt[3]{-8}\text{=}-2$.

For a non-zero complex number a, there are n complex numbers z such that zⁿ =  a, which may also be referred to as nth roots of a. In the Argand diagram these nth roots form the vertices of a regular n-gon.