# How do you find all the real cube roots of 8/125?

##### 1 Answer

Oct 19, 2015

#### Explanation:

#8 = 2^3# and#125 = 5^3#

So

#root(3)(8/125) = root(3)(2^3/125^3) = root(3)(2^3)/root(3)(5^3) = 2/5#

The other two roots are both Complex:

#2/5 omega = 2/5((-1+i sqrt(3))/2) = (-1+i sqrt(3))/5#

#2/5 omega^2 = 2/5((-1+i sqrt(3))/2) = (-1-i sqrt(3))/5#

where