Definition:Root (Analysis)

Definition
Let $x \in \R$ be a real number.

Let $m \in \Z$ be an integer such that $m \ne 0$.

If $y \in \R$ and $y^m = x$, then $y$ is called an $m$th root of $x$.

By Existence of Root, each $x \ge 0$ has a unique positive $m$th root, $y$.

This $y$ is called the positive $m$th root of $x$, and is denoted $y = \sqrt [m] x$.

The $2$th roots of a number are called square roots.

The positive square root of $x$ is written $\sqrt x$.

By Integral Power Function Bijective iff Index Odd, each real number has exactly one real $3$th root.

The $3$th roots of a number are called cube roots.

The positive $m$th root of $x$ can also be written, using the power notation, as $x^{1/m}$.

Also see

 * Power