How do you simplify $sqrt84 * sqrt28$ ?

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How do you simplify $sqrt84 * sqrt28$ ?

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Answer 1 · 2016-04-30T07:23:22

$sqrt(84)*sqrt(28)=sqrt(28^2*3)=28sqrt(3)$

Explanation:

Here's a factor tree for $28$ :

$color(white)(0000)28$
$color(white)(000)"/"color(white)(00)"\"$
$color(white)(00)2color(white)(000)14$
$color(white)(00000)"/"color(white)(00)"\"$
$color(white)(0000)2color(white)(0000)7$

So: $28 = 2^2*7$

$color(white)()$
Here's a factor tree for $84$ :

$color(white)(0000)84$
$color(white)(000)"/"color(white)(00)"\"$
$color(white)(00)2color(white)(000)42$
$color(white)(00000)"/"color(white)(00)"\"$
$color(white)(0000)2color(white)(000)21$
$color(white)(0000000)"/"color(white)(00)"\"$
$color(white)(000000)3color(white)(0000)7$

So: $84 = 2^2*3*7 = 28*3$

$color(white)()$
So:

$sqrt(84)*sqrt(28)=sqrt(84*28)=sqrt(28^2*3)=28sqrt(3)$

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