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

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

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Answer 1 · 2016-08-22T10:27:34

$60 - 42 \sqrt{5}$ $60-42sqrt5$

Explanation:

$Tip about formatting$ $color(blue)("Tip about formatting")$
the format command for radical is hash sqrt(20) hash giving $\sqrt{2}$ $sqrt(2)$ .

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

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

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

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

$3 \sqrt{20} . (2 \sqrt{5} - 7)$ $" " 3sqrt(20) color(white)(.) (2sqrt(5)-7)$

I wanted the 20 to stand out so I wrote:

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

$3 \sqrt{20} . (2 \sqrt{5} - 7)$ $" " 3sqrt(color(red)(20)) color(white)(.) (2sqrt(5)-7)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Answering the question$ $color(blue)("Answering the question")$

Note that $4 \times 5 = 20 \to 2^{2} \times 5 = 20$ $4xx5=color(red)(20) -> 2^2xx5=color(red)(20)$

$3 \sqrt{2^{2} \times 5} . (2 \sqrt{5} - 7)$ $3sqrt(2^2xx5)color(white)(.)(2sqrt(5)-7)$

$3 \times 2 \sqrt{5} . (2 \sqrt{5} - 7)$ $3xx2sqrt(5)color(white)(.)(2sqrt(5)-7)$

$6 \sqrt{5} . (2 \sqrt{5} - 7)$ $6sqrt(5)color(white)(.)(2sqrt(5)-7)$

Note that $6 \sqrt{5} \times 2 \sqrt{5} = (6 \times 2) \times {(\sqrt{5} .)}^{2} = 12 \times 5$ $6sqrt5xx2sqrt5 = (6xx2)xx(sqrt5color(white)(.))^2 =12xx5$

$(12 \times 5) - 42 \sqrt{5}$ $(12xx5)-42sqrt(5)$

$60 - 42 \sqrt{5}$ $60-42sqrt5$

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

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