The k-th Root and the Square Root of a Nonnegative Real Number

In the setting of The Real Numbers, with the Natural Numbers, Integers and Rationals Identified with Subsets of the Reals, and Completeness, let $k\in\mathbb{N}$ and $x\in\mathbb{R}$ with $x\ge0$.

¶ The $k$-th root of $x$, written $\sqrt[k]{x}$, is the $y\in\mathbb{R}$ with $y\ge0$ and $y^{k}=x$, which exists and is unique by Existence and Uniqueness of Nonnegative k-th Roots of Nonnegative Real Numbers §root.

¶ The square root of $x$ is $\sqrt{x}=\sqrt[2]{x}$.