# How do you simplify sqrt84 * sqrt28?

Apr 30, 2016

$\sqrt{84} \cdot \sqrt{28} = \sqrt{{28}^{2} \cdot 3} = 28 \sqrt{3}$

#### Explanation:

Here's a factor tree for $28$:

$\textcolor{w h i t e}{0000} 28$
$\textcolor{w h i t e}{000} \text{/"color(white)(00)"\}$
$\textcolor{w h i t e}{00} 2 \textcolor{w h i t e}{000} 14$
$\textcolor{w h i t e}{00000} \text{/"color(white)(00)"\}$
$\textcolor{w h i t e}{0000} 2 \textcolor{w h i t e}{0000} 7$

So: $28 = {2}^{2} \cdot 7$

$\textcolor{w h i t e}{}$
Here's a factor tree for $84$:

$\textcolor{w h i t e}{0000} 84$
$\textcolor{w h i t e}{000} \text{/"color(white)(00)"\}$
$\textcolor{w h i t e}{00} 2 \textcolor{w h i t e}{000} 42$
$\textcolor{w h i t e}{00000} \text{/"color(white)(00)"\}$
$\textcolor{w h i t e}{0000} 2 \textcolor{w h i t e}{000} 21$
$\textcolor{w h i t e}{0000000} \text{/"color(white)(00)"\}$
$\textcolor{w h i t e}{000000} 3 \textcolor{w h i t e}{0000} 7$

So: $84 = {2}^{2} \cdot 3 \cdot 7 = 28 \cdot 3$

$\textcolor{w h i t e}{}$
So:

$\sqrt{84} \cdot \sqrt{28} = \sqrt{84 \cdot 28} = \sqrt{{28}^{2} \cdot 3} = 28 \sqrt{3}$