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

2 Answers
Alan P.
Jul 10, 2015

#-(45sqrt(3)+30)#

Explanation:

#-3sqrt(5)(3sqrt(15)+2sqrt(5))#
#color(white)("XXXX")##=(-3sqrt(5) * 3sqrt(15)) + (-3sqrt(5) * 2sqrt(5))#

#color(white)("XXXX")##=-9sqrt(75) - 6 sqrt(25)#

#color(white)("XXXX")##=-9*5sqrt(3) -6*5#

#color(white)("XXXX")##=-(45sqrt(3)+30)#

Meave60
Jul 10, 2015

The answer is #-45sqrt3-30#.

Explanation:

#-3sqrt5(3sqrt(15)+2sqrt5)#

Distribute the #-3sqrt5# by multiplying it times both terms in the parentheses.

#-9sqrt5sqrt15-6sqrt5sqrt5# =

Simplify.

#-9sqrt5sqrt3sqrt5-6sqrt5sqrt5# =

Simplify.

#(sqrt5sqrt5=5)#

#-9*5sqrt3-6*5# =

Simplify.

#-45sqrt3-30#

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