What is the simplest radical form of #-4 sqrt(6) / sqrt(27)#?

1 Answer
Jul 23, 2015

Answer:

#(-4sqrt(2))/3#

Explanation:

To get the simplest radical form for this expression, you need to check to see if you can simplify some of the terms, more specifically some of the radical terms.

Notice that you can write

#-4sqrt(6)/(sqrt(9 * 3)) = (-4sqrt(6))/(3sqrt(3))#

You can simplify #sqrt(3)# from both the denominator and the numerator to get

#(-4 * sqrt(2 * 3))/(3 sqrt(3)) = (-4 * sqrt(2) * cancel(sqrt(3)))/(3cancel(sqrt(3))) = color(green)((-4sqrt(2))/3)#