How do you simplify #(5sqrt3) /( 6sqrt10)#?

1 Answer
Jul 25, 2015

Answer:

You rationalize the denominator and check to see if you can cancel any of the terms out.

Explanation:

The first thing you need to do in order to simplify this expression is to rationalize the denominator.

You can do that by multiplying the numerator and the denominator by #sqrt(10)#

#(5 * sqrt(3) * sqrt(10))/(6 * sqrt(10) * sqrt(10))#

Now use the product property of radicals to get

#( 5 * sqrt(3 * 10))/(6 * sqrt(10 * 10)) = (5 * sqrt(30))/(6 * 10) = (5 * sqrt(30))/(6 * 2 * 5)#

This is equivalent to

#(cancel(5) * sqrt(30))/(6 * 2 * cancel(5)) = color(green)(sqrt(30)/12)#