How do you simplify #3sqrt18+3sqrt12+2sqrt27#?

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Answer 1 · 2016-08-22T01:01:40

#9sqrt2 +12sqrt3#

Write each number as the product of its prime factors first.
Look for squares of factors.

#3sqrt18 = 3 xxsqrt(2xx3xx3) = 3xx3sqrt2#

#3sqrt12 = 3 xxsqrt(2xx2xx3) = 3xx2sqrt3#

#2sqrt27 = 2xxsqrt(3xx3xx3) = 2xx3sqrt3#

#3sqrt18 + 3sqrt12 + 2sqrt27#

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

=#9sqrt2 + color(red)(12sqrt3)#