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

1 Answer
Aug 11, 2016

=sqrt2(-3-2sqrt3)

Explanation:

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)