How do you find the nearest hundredth of the cub roots:
8 cube root and 75 cube root

Part 1 
To the nearest hundredth: 
cubed root of 103 is 4.687... rounded gives 4.69 

Part 2 :now as to the process : 
its going to be repeated power finding on a calculator, or by hand : 
4x4x4 = 64 
5x5x5 = 125 so its between 4 and 5 
4.5 x 4.5 x4.5 = 91.1 
4.6 x 4.6 x 4.6 = 97.3 so its a little higher 
4.65 x 4.65 x 4.65 = 100.5 needs to be higher still 
so we continue until we get to 4.68 
4.68 x 4.68 x 4.68 = 102.5 too low 
4.69 x 4.69 x 4.69 = 103.1 too high 
so continue : 
try 4.681 , 4.682 , and so on 
until we get 4.687 x 4.687 x 4.687 = 102.96 ( pretty close ) 
and 4.688 x 4.688 x 4.688 = 103.02 ( slightly too high ) 
and continue with the next decimal .. 
and eventually 
4.687 is the closest ... Rounded gives 4.69