How do you simplify -2√27-3√27+3√18?

1 Answer
Aug 20, 2015

=color(blue)(-15sqrt3+9sqrt2=153+92

Explanation:

-2sqrt27 -3sqrt27+3sqrt18227327+318

=-5sqrt27+3sqrt18=527+318

Simplifying by prime factorisation
sqrt27=sqrt(3*3*3)=sqrt(3^2*3)=color(blue)(3sqrt327=333=323=33

sqrt18=sqrt(3*3*2) =sqrt(3^2*2)=color(blue)(3sqrt218=332=322=32

Our expression now becomes:
=-5*color(blue)(3sqrt3) +3*color(blue)(3sqrt2=533+332

=-15sqrt3+9sqrt2=153+92