How do you calculate a square root without a calculator? I know there is some method based on iterations and the Taylor series. Someone told me about a method that resembles long division and doesn’t require iterations, but he can’t remember how it works.

The only way I know is to do the iterations … divide the number by a smaller number, and keep adjusting your divisor until it equals (or nearly equals) the quotient. It shouldn’t take too long to get a few decimal’s worth of accuracy.

I learned this method in grade school. I was going to retype it in, but fortunately found an explanation on the web.

La franchise ne consiste pas à dire tout ce que l’on pense, mais à penser tout ce que l’on dit.

H. de Livry

Cool! I had learned that in school too, but forgot how. Thanks!