\begin{definition}[Definition:Root (Analysis)]
Let $x, y \in \R_{\ge 0}$ be positive real numbers.
Let $n \in \Z$ be an integer such that $n \ne 0$.
Then $y$ is the '''positive $n$th root of $x$''' {{iff}}:
:$y^n = x$
and we write:
:$y = \sqrt[n] x$
Using the power notation, this can also be written:
:$y = x^{1/n}$
When $n = 2$, we write $y = \sqrt x$ and call $y$ the '''positive square root''' of $x$.
When $n = 3$, we write $y = \sqrt [3] x$ and call $y$ the '''cube root''' of $x$.
Note the special case where $x = 0 = y$:
:$0 = \sqrt [n] 0$
\end{definition}