We can handle this with the function . Since this can be evaluated exactly at x = 32 , we can use differentials to determine the change in the root when the value of x changes by 0.5:

Evaluating this at x = 32, we have

Hence the fifth root of 32.5 can be found using this change in the root:

For comparison, taking the root directly on a calculator, we get 2.00621.