# Teaching Tidbit: Calculating Square Roots by Hand

This topic chosen to satisfy an e-mail request. It is entirely possible to calculate square roots without the aid of an electronic or mechanical device more advanced than a pencil. More on this, and about choosing content, frequency, and presentation of these lessons comes after the break.

The complete details for calculating square roots by hand can be found here.

As mentioned before, if there are any topics in physics, math or education you’d like to learn more about, let me know, either in the comments or by e-mail. If I don’t know how to do something already, I’ll probably be willing to learn. (I’ll also pay attention to “me too!” posts supporting the same idea.)

Questions for readers: how often do you want these columns to appear? If there seem to be enough topics to keep things on a semi-regular schedule, would you like that, or should I stick to the (more manageable) schedule of doing the columns as the requests come in and my time allows, so they’d end up coming out at random intervals? Also, would you like to see the columns collected on a sidebar page with the event calendar, chatroom link, and so forth? In short, what do you want these columns to become?

## 8 replies on “Teaching Tidbit: Calculating Square Roots by Hand”

1. pythor says:

Personally, I’d take them as fast as you feel like posting them. I’m greedy like that ;)

This is similar to a method I learned in high school, though easier and more intuitive. I was hoping it might be the method I learned in grade school. I’ve forgotten that method, and have never been able to find a description of it when I tried. All I remember is that it looked a lot like long division, but when you brought down zeros, you had to bring down two at a time. Your method is definitely easier to remember, though I couldn’t tell you how fast my grade school method gave accurate results.

• I’m not familiar with the method you’re describing. I expect there will be another tidbit (about manual calculation of logarithms, including two different methods) appearing either Monday night or Tuesday. Less than a week after that, and I should have something up about calculating greatest common factors using subtraction only.

2. TomSwiss says:

pthyor: I too have hazy memories of a long-division like method for working out square roots that (IIRC) gave one digit at a time.

3. pythor says:

I think the various links here do point to the algorithm I was taught in school. That said, not one of those links explains the method in a way that I will remember the next time I decide I need to calculate one. On the other hand, the method given here, apparently named the Babylonian method, is simple and intuitive.

I have no idea where I learned the method I’ve generally used in the past. It is similar to the method described here, but instead of using the average of the guess and the answer/guess, I used a fraction calculated from the difference between the guess squared and the answer. I may have invented it on the spot one day, for all I know. It was never very efficient.

• The first time I saw the long division-like method was when I looked it up and posted that link. One of these days I’m going to sit down and reverse engineer the thing to figure out WHY it works. Research shows that there’s little or no retention of knowledge gained if the student doesn’t understand why what he/she learns is correct. That’s part of my problem, and it’s likely why you expect to forget it shortly.

I’ve very big on the “why” part of math, science, etc. It makes a big difference in both learning and teaching.