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

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Answer 1 · 2015-07-25T11:14:26

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

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)#