Question

How do you use Newton's Method to approximate `root5(20)` ?

Answer 1

Start with values: Low `< root(5)(20)` and High `> root(5)(20)`; find Midpoint; replace either the Low or High value depending upon whether `"(Midpoint)"^5` is greater than or less than 20. Repeat.

Explanation:

(see image below where the above process was performed on a spreadsheet)

Note that this process can be repeated until the `("Midpoint")^5` is as close as desired to `20`

If `("Midpoint")^5 ~= 20`
then
`color(white)("XXXX")root(5)(20) ~= "Midpoint"`