Computing the Cube root of a decimal number manually.

What we have here are decimals, which makes the process a little more difficult.

Make 72.14 into an improper fraction, distribute the cube root to the number and denominator, then all you do from there is break the numbers down into there factors and cube root following that

93.65

= 93 65/100

= 9365/100

apply the 3rd root

\(\frac{\sqrt[3]{9365}}{\sqrt[3]{100}}\)

100 breaks down into factors 2*2*5*5, but unfortunately no combination of these factors gives a product that a perfect cube, so the answer would have to be between 4 and 5.

Helps to know your perfect cubes

Using the calculator, it's \(\sqrt[3]{100}=4.641588834\). So you'd have to narrow it down decimal by decimal until you get it. Really sucks, doesn't it?



anyway, let me know if you need further guidance