How do you simplify #-2sqrt15(-3sqrt3+3sqrt5)#?

2 Answers
smendyka
Aug 18, 2017

See a solution process below:

Explanation:

First, multiply each term within the parenthesis by the term outside the parenthesis:

#color(red)(-2sqrt(15))(-3sqrt(3) + 3sqrt(5)) =>#

#(color(red)(-2sqrt(15)) xx -3sqrt(3)) + (color(red)(-2sqrt(15)) xx 3sqrt(5)) =>#

#(color(red)(-2) xx -3)color(red)(sqrt(15))sqrt(3) + (color(red)(-2) xx 3)color(red)(sqrt(15))sqrt(5) =>#

#6sqrt(15 xx 3) + (-6)sqrt(15 xx 5) =>#

#6sqrt(45) - 6sqrt(75)#

Now, we can simplify the radicals:

#6sqrt(45) - 6sqrt(75) =>#

#6sqrt(9 xx 5) - 6sqrt(25 xx 3) =>#

#6sqrt(9)sqrt(5) - 6sqrt(25)sqrt(3) =>#

#(6 * 3)sqrt(5) - (6 * 5)sqrt(3) =>#

#18sqrt(5) - 30sqrt(3)#

Pop Quiz Whiz
Aug 18, 2017

#18 sqrt(5) - 30 sqrt(3)#

Explanation:

First, distribute the #-2sqrt(15)#
You end up with:
#6 sqrt(45) - 6 sqrt(75)#
You can then factor under the radical.
#6sqrt(9*5) - 6sqrt(25*5)#
Then, simplify by square rooting the perfect squares.
#6*3 sqrt(5) - 6*5 sqrt(3)#
Then multiply.
#18 sqrt(5) - 30 sqrt(3)#

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