Absolute Value Equals Square Root of Square

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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 $x^2$.


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