How do you find the nearest hundredth of the cub roots:

8 cube root and 75 cube root

8 Cube root: 2

75 Cube root: 4.22

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