How do you simplify #-3sqrt18+3sqrt8-sqrt24#?

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Answer 1 · 2016-08-11T19:27:10

=#sqrt2(-3-2sqrt3)#

Find each number as the product of its prime factors and see what we are working with. Factors in pairs have a square root.

#-3sqrt18 +3sqrt8-sqrt24#

=#-3sqrt((3xx3)xx2) +3sqrt((2xx2)xx2) -sqrt((2xx2)xx2xx3)#

=#-3xx3color(red)(sqrt2)+3xx2color(red)(sqrt2)-2color(red)(sqrt2)sqrt3#

There is a common factor, factorise:

=#color(red)(sqrt2)(-9+6-2sqrt3)#

=#sqrt2(-3-2sqrt3)#