How do you simplify -2√27-3√27+3√18?

1 Answer
Don't Memorise
Aug 20, 2015

#=color(blue)(-15sqrt3+9sqrt2#

Explanation:

#-2sqrt27 -3sqrt27+3sqrt18#

#=-5sqrt27+3sqrt18#

Simplifying by prime factorisation
#sqrt27=sqrt(3*3*3)=sqrt(3^2*3)=color(blue)(3sqrt3#

#sqrt18=sqrt(3*3*2) =sqrt(3^2*2)=color(blue)(3sqrt2#

Our expression now becomes:
#=-5*color(blue)(3sqrt3) +3*color(blue)(3sqrt2#

#=-15sqrt3+9sqrt2#

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