How do you simplify #(6 sqrt 5) div (5 sqrt 3)#?

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Answer 1 · 2016-03-05T16:21:30

#(2sqrt15)/5#

To simplify

#=(6sqrt5)/(5sqrt3)#

We should "rationalize" the denominator. This means, try to get the #sqrt3# out of the denominator.

We can do this by multiplying the fraction by #sqrt3/sqrt3#.

#=(6sqrt5)/(5sqrt3)(sqrt3/sqrt3)#

In the numerator, we use the rule that #sqrtasqrtb=sqrt(ab)#, so #sqrt5sqrt3=sqrt15#.

In the denominator, we see that #sqrt3sqrt3=3#, so the square root has been eliminated from the denominator.

#=(6sqrt15)/(5*3)#

Simplify the fraction:

#=(2sqrt15)/5#