How do you simplify #sqrt((5c^5)/(4d^5))#?

1 Answer
May 30, 2017

Answer:

#color(blue)((c^2sqrt(5cd))/(2d^3)#

Explanation:

#sqrt((5c^5)/(4d^5))#

#:.=(sqrt(5c^5))/(sqrt(4d^5))#

#:.=sqrt(5*c*c*c*c*c)/sqrt(2*2*d*d*d*d*d)#

#:.=(c^2sqrt(5c))/(2d^2sqrtd)#

#:.=(c^2sqrt(5c))/(2d^2sqrtd) xx (2d^2sqrtd)/(2d^2sqrtd #

#:.=(cancel2^color(blue)1c^2cancel(d^2)sqrt(5cd))/(cancel4^color(blue)2cancel(d^5)^3#

#:.color(blue)(=(c^2sqrt(5cd))/(2d^3)#