# How do you express the product of 3[radical 20](2[radical 5] - 7) in simplest radical form?

##### 1 Answer
Aug 22, 2016

$60 - 42 \sqrt{5}$

#### Explanation:

$\textcolor{b l u e}{\text{Tip about formatting}}$
the format command for radical is hash sqrt(20) hash giving $\sqrt{2}$.

So you would write: hash 3sqrt(20)(2sqrt(5)-7) hash giving:

$3 \sqrt{20} \left(2 \sqrt{5} - 7\right)$

Or you could put a space in using "" or color(white)(.)

hash 3sqrt(20) color(white)(.) (2sqrt(5)-7)hash

$\text{ } 3 \sqrt{20} \textcolor{w h i t e}{.} \left(2 \sqrt{5} - 7\right)$

I wanted the 20 to stand out so I wrote:

hash" " 3sqrt(color(red)(20)) color(white)(.) (2sqrt(5)-7) hash

$\text{ } 3 \sqrt{\textcolor{red}{20}} \textcolor{w h i t e}{.} \left(2 \sqrt{5} - 7\right)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Answering the question}}$

Note that $4 \times 5 = \textcolor{red}{20} \to {2}^{2} \times 5 = \textcolor{red}{20}$

$3 \sqrt{{2}^{2} \times 5} \textcolor{w h i t e}{.} \left(2 \sqrt{5} - 7\right)$

$3 \times 2 \sqrt{5} \textcolor{w h i t e}{.} \left(2 \sqrt{5} - 7\right)$

$6 \sqrt{5} \textcolor{w h i t e}{.} \left(2 \sqrt{5} - 7\right)$

Note that $6 \sqrt{5} \times 2 \sqrt{5} = \left(6 \times 2\right) \times {\left(\sqrt{5} \textcolor{w h i t e}{.}\right)}^{2} = 12 \times 5$

$\left(12 \times 5\right) - 42 \sqrt{5}$

$60 - 42 \sqrt{5}$