# Q&A: Why is Newton’s Method Useful?

by Justin Skycak on

Cross-posted from here.

## Question

If you teach Newton’s method for finding roots of real functions on the high school (or freshmen) level, I think some students may reason like a variant of the following:

Why do I need learn such a “complicated” method if I simply can use the following?

• plot it, for example, via Geogebra, and zoom in and just read off the root to the desired precision
• or just use the table value function of my calculator and do some kind of interval nesting

What would be good examples or activities to make it clear that the Newton method is useful and in some ways better than the approaches above? How can I explain where it makes sense to use Newton’s method over the more simple methods above?

How can you estimate $\sqrt[3]{2}$ without directly using fractional exponents?
The most straightforward option is to use bisection search, but Newton’s method (finding the root of $x^3-2$ is faster). Here is the problem set I had them do.