How do you simplify #sqrt(-75)^3#?

Question

3286 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-16T13:24:27

#color(blue)(i375sqrt(3))#

#sqrt((-75)^3)=sqrt(-1)*sqrt(75^3)#

#:.#

#sqrt(75^3)=(75)^(3/2)=(sqrt(75))^3=(sqrt(3xx25))^3=(5sqrt(3))^3#

#=5^3(sqrt(3))^3=3*5^3sqrt(3)=375sqrt(3)#

#:.#

#375sqrt(3)*sqrt(-1)=i375sqrt(3)#

#color(blue)(i375sqrt(3))#