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))#