How do you simplify sqrt(5x - 3)^2?

Jun 28, 2015

${\left(\sqrt{5 x - 3}\right)}^{2} = 5 x - 3$

Explanation:

Squaring a positive value and taking the (positive) square root are inverse operations.

Note however that
$\textcolor{w h i t e}{\text{XXXX}}$$\sqrt{{\left(5 x - 3\right)}^{2}}$ is not necessarily equal to $\left(5 x - 3\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$\sqrt{{\left(5 x - 3\right)}^{2}} = \left\mid 5 x - 3 \right\mid$

One other possibility that might have been intended is
$\textcolor{w h i t e}{\text{XXXX}}$$\sqrt{5 x - \left({3}^{2}\right)}$
but this has no interesting simplifications other than
$\textcolor{w h i t e}{\text{XXXX}}$$\sqrt{5 x - 9}$