Question

How do you simplify -2√27-3√27+3√18?

Answer 1

`=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`