How do you simplify #sqrt(162x^6)/sqrt(64x^2)#?

1 Answer
Jul 1, 2015

Answer:

#(sqrt(162x^6))/(sqrt(64x^2))= 9/8 x sqrt(2)#

Explanation:

Factoring #162x^6#
#color(white)("XXXX")##= 2xx(81) xx (x^3)^2#
#color(white)("XXXX")##= 2xx (9x^3)^2#

#sqrt(162x^6)#
#color(white)("XXXX")##=sqrt(2xx(9x^3)^2)#
#color(white)("XXXX")##=9x^3sqrt(2)#

Factoring #64x^2#
#color(white)("XXXX")##=(8x)^2#

#sqrt(64x^2)#
#color(white)("XXXX")##=sqrt((8x)^2)#
#color(white)("XXXX")##=8x#

#(sqrt(162x^6))/(sqrt(64x^2)#
#color(white)("XXXX")##= (9x^3sqrt(2))/(8x)#

#color(white)("XXXX")##= 9/8 x^2 sqrt(2)#