nth root ($\sqrt[k]{n}$)

An $n$th root of $a$ is a solution of $x^n=a$, where $n$ is a positive integer. For $a\ge 0$ there is a unique nonnegative real root, denoted $\sqrt[n]{a}$. For odd $n$ each real number has exactly one real root; for even $n$, a positive input has two real solutions and a negative input has none.

For example, $\sqrt[4]{16}=2$ denotes the principal nonnegative root, although both $2$ and $-2$ solve $x^4=16$. Over the complex numbers, a nonzero $a$ has $n$ distinct roots, differing by $n$th roots of unity. Specifying the field and the principal-root convention prevents ambiguity.