How do you simplify #7sqrt3-4sqrt6+sqrt48-sqrt54#?

1 Answer
Jan 5, 2017

Answer:

#23sqrt(3)-7sqrt(6)#

Explanation:

Note:
#color(white)("XXX")color(green)(sqrt(6))=color(green)(sqrt(2)) * color(magenta)(sqrt(3))#
#color(white)("XXX")color(red)(sqrt(48))=color(red)(sqrt(16)) * color(magenta)(sqrt(3)) = color(red)(4) * color(magenta)(sqrt(3))#
#color(white)("XXX")color(blue)(sqrt(54))=color(blue)(sqrt(9) * sqrt(2)) * color(magenta)(sqrt(3))=color(blue)(3sqrt(2)) * color(magenta)(sqrt(3))#

Therefore:
#7color(magenta)(sqrt(3))-4color(green)(sqrt(6))+4color(red)(sqrt(48))-color(blue)(sqrt(54))#

#=color(magenta)(sqrt(3)) * ( 7 -4color(green)(sqrt(2))+4 *color(red)(4)-color(blue)(3sqrt(2)))#

#=color(magenta)(sqrt(3))(23-7sqrt(2))#

or
#=23sqrt(3)-7sqrt(6)#