How do you simplify 12 (sqrt of 2) divided by 2 (sqrt of 27)?

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Answer 1 · 2015-10-09T00:18:04

$2/3 * sqrt(6)$

Assuming that your starting expression looks like this

$(12sqrt(2))/(2sqrt(27))$

you can start by writing

$(12sqrt(2))/(2sqrt(27)) = (6sqrt(2))/sqrt(27)$

Now focus on $sqrt(27)$ . Notice that you can write $27$ as

$27 = 3 * 9 = 3^2 * 3$

This means that you have

$sqrt(27) = sqrt(3^2 * 3) = 3sqrt(3)$

The expression becomes

$(6sqrt(2))/(3sqrt(3)) = (2sqrt(2))/sqrt(3)$

Rationalize the denominator by multiplying the fraction by $1 = sqrt(3)/sqrt(3)$

$(2sqrt(2))/sqrt(3) * sqrt(3)/sqrt(3) = (2 * sqrt(2) * sqrt(3))/(sqrt(3) * sqrt(3)) = color(green)(2/3sqrt(6))$