What is the simplest radical form of #-2sqrt96#?

1 Answer
Jul 23, 2015

Answer:

#-2sqrt(96) = -8sqrt(6)#

Explanation:

Factoring #96#
#color(white)("XXXX")##=2xx48#
#color(white)("XXXX")##=2^2xx24#
#color(white)("XXXX")##=2^2xx2xx12#
#color(white)("XXXX")##=2^2xx2^2xx6#
#color(white)("XXXX")##=2^2xx2^2xx2xx3#

#sqrt(96)#
#color(white)("XXXX")##= sqrt(2^2xx2^2xx2xx3)#
#color(white)("XXXX")##=sqrt(2^2)xxsqrt(2^2) xxsqrt(2xx3)#
#color(white)("XXXX")##=2xx2xxsqrt(6)#
#color(white)("XXXX")##=4sqrt(6)#

#-2sqrt(96)#
#color(white)("XXXX")##=(-2)xx(4sqrt(6))#
#color(white)("XXXX")##=-8sqrt(6)#