# How do you simplify sqrt(24x)*sqrt(6x)?

May 19, 2018

$12 x$

#### Explanation:

Given: $\sqrt{24 x} \times \sqrt{6 x}$

Note that 24 is the same as $4 \times 6 \to {2}^{2} \times 6$

So if we 'split up' the roots we have:

$\textcolor{w h i t e}{\text{ddddddd}} \sqrt{{2}^{2}} \times \sqrt{6} \times \sqrt{x} \times \sqrt{6} \times \sqrt{x}$

Grouping the values:

$\textcolor{w h i t e}{\mathrm{dd} \mathrm{dd} \mathrm{dd} \text{d}} \sqrt{{2}^{2}} \times \underbrace{\sqrt{6} \times \sqrt{6}} \times \underbrace{\sqrt{x} \times \sqrt{x}}$

color(white)(dddddd"ddd")ubrace(2color(white)("ddddd")xx6color(white)("dddddd")xx x)

$\textcolor{w h i t e}{\mathrm{dd} \mathrm{dd} \mathrm{dd} \text{ddddddddddd}} 12 x$

May 19, 2018

$12 x$

#### Explanation:

$\sqrt{24 x} \cdot \sqrt{6 x}$

$\therefore = \sqrt{2 \cdot 2 \cdot 2 \cdot 3 x} \cdot \sqrt{6 x}$

$\sqrt{2} \cdot \sqrt{2} = 2$

$\therefore = 2 \sqrt{6 x} \cdot \sqrt{6 x}$

$\therefore = \sqrt{6} x \cdot \sqrt{6} x = 6 x$

$\therefore = 2 \cdot 6 x$

$\therefore = 12 x$