Existence and Uniqueness of Positive Root of Positive Real Number

Theorem
Let $x \in \R$ be a real number such that $x \ge 0$.

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

Then there always exists a unique $y \in \R: \left({y \ge 0}\right) \land \left({y^n = x}\right)$.

Hence the justification for the terminology the positive $n$th root of $x$ and the notation $x^{1/n}$.

Proof
The result follows from Existence of Positive Root and Uniqueness of Positive Root.