Absolute Value Equals Square Root of Square

From ProofWiki
Jump to navigation Jump to search

Theorem

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

Let $\size x$ be its absolute value.


Then $\size x = \sqrt {x^2}$, 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 $x^2 \ge 0$.