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
