How do you simplify $sqrt3(sqrt12-sqrt6)$ ?

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Answer 1 · 2015-11-09T08:43:02

First, expand the product: multiply $sqrt(3)$ with $sqrt(12)$ and with $sqrt(6)$ , respectively:

$sqrt(3)(sqrt(12) - sqrt(6)) = sqrt(3) * sqrt(12) - sqrt(3) * sqrt(6)$

Now, use the rule $sqrt(a*b) = sqrt(a) * sqrt(b)$ :

$sqrt(3) * sqrt(12) - sqrt(3) * sqrt(6)$
$= sqrt(3 * 12) - sqrt(3 * 6)$
$= sqrt(36) - sqrt(18)$
$= 6 - sqrt(18)$

The last one, $sqrt(18)$ , can be simplifyed further since $18 = 2 * 9$ and $9 = 3^2$ :

$6 - sqrt(18)$
$= 6 - sqrt(2*9)$
$= 6 - sqrt(2)*sqrt(9)$
$= 6 - sqrt(2)*3$
$= 6 - 3sqrt(2)$

I hope that this helped!

How do you simplify sqrt3(sqrt12-sqrt6)sqrt3(sqrt12-sqrt6)?