How do you simplify #sqrt(27) - sqrt(8) + 2 sqrt(2)#?

2 Answers

It is

#sqrt(27) - sqrt(8) + 2 sqrt(2)=3*sqrt3-2sqrt2+2sqrt2=3*sqrt3#

Feb 28, 2016

Answer:

#3sqrt(3)#

Explanation:

Since
#color(white)("XXX")color(red)(sqrt(27) = sqrt(3^2*3) = 3sqrt(3))#
and
#color(white)("XXX")color(blue)(sqrt(8) = sqrt(2^2*2) = 2sqrt(2))#

Therefore
#color(white)("XXX")color(red)(sqrt(27)-color(blue)(sqrt(8) + color(green)(2sqrt(2)#

#color(white)("XXX")= color(red)(3sqrt(3))cancel(-color(blue)(2sqrt(2)))cancel(+color(green)(2sqrt(2)))#

#color(white)("XXX")=3sqrt(3)#