= nth root
{title2=$\sqrt[k]{n}$}
An $n$th root of $a$ is a solution of $x^n=a$, where $n$ is a positive <integer>. For $a\ge0$ 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.
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