How do you simplify #sqrt(54a^9)#?

1 Answer
Jul 1, 2015

Answer:

#sqrt(54a^9) = 3a^4sqrt(6a)#
#color(white)("XXXX")#(of course, it is debatable whether this is really simpler).

Explanation:

Factoring #54a^9#
#color(white)("XXXX")##54a^9 = (9*6)(a^8*a)#
#color(white)("XXXX")##color(white)("XXXX")##=(3^2*6)((a^4)^2*a)#
#color(white)("XXXX")##color(white)("XXXX")##=(3a^4)^2*(6a)#

#sqrt(54a^9)#
#color(white)("XXXX")##=sqrt((3a^4)^2*(6a))#

#color(white)("XXXX")##=sqrt((3a^4)^2) *sqrt(6a#

#color(white)("XXXX")##=3a^4*sqrt(6a)#