# Absolute Value Equals Square Root of Square

From ProofWiki

This article has been proposed for deletion. In particular: It's not completely certain exactly what the purpose of this aborted refactoring was |

## Theorem

Let $x \in \R$ be a real number.

Let $|x|$ be its absolute value.

Then $|x| = \sqrt{x^2}$, where:

- $x^2$ is the square of $x$
- $\sqrt{x^2}$ is the square root of $x^2$.

## Proof

Note that by Square of Real Number is Positive, indeed $x^2 \ge 0$.