![]() ![]() Subtract n^2 from the pair to get remainder.Ĭreate next BAL by appending next-2-digits to remainder. ![]() Start with left-most pair (or single left-over digit.)įind largest n such that n^2 less-than-or-equal the pair. Group NTBR in pairs from the decimal point. Square Root - pencil/paper digit by digit methodĪSF = answer so far, ignoring any decimal point I came up with aįairly compact description that relies on a somewhat algebraic ![]() It was hard to remember and it'sįairly difficult to describe in words alone. In fact, I wonder if it's not alreadyĮssentially lost except for those who study ancient methods. I doubt that they teach the process any more. You might still have a problem finding an exact root of a very Personal calculators have largely eliminated that need, When I was going to school, one mark of an educated person was theĪbility to find a square root with pencil and paper. It mighty be of passing interest to this forum. This post reminded me of something I wrote for my kids a while back. In response to message #1 by Thomas Klemm Message #2 Posted by Bob Patton on, 9:00 p.m., US Patent 3576983: DIGITAL CALCULATOR SYSTEM FOR COMPUTING SQUARE ROOTS MEGGIT, Pseudo Division and Pseudo Multiplication processes, IBM Journal, Res & Dev, April 1962, 210-226. It's quiet amazing that the same algorithm was used in all these calculators over the years with only minor changes. Personally I consider this algorithm a beautiful pearl. Unfortunately Cochran's trick won't work in these cases. The same algorithm could be used to solve the cubic root or x 2 = x + 1. Thus our unit becomes one tenth of what it was before. We move our coordinate system step by step to the right until we step over the root. We could have also used a separate counter but it's not necessary. Now Cochran's trick becomes evident: In the second column appears the result 6.40312. Here I assume you're familiar with the Horner scheme:įrom now on I've chosen a shorter format: We can use Horner's method to calculate the remainders. Thus by continued polynominal division we can get the coefficients of the transformed polynominal. What happens to a quadratic equation if we apply these transformations? Now let's consider the following simple coordinate transformations: Let's assume we want to calculate the square root of 41 thus solving the equation:įirst we apply a trick which can be found in Cochran's patent and multiply the whole equation by 5: While this might be obvious to some of you I only recently realized that the method used to calculate the square root in probably most HP-calculators is in fact closely related to Horner's method. Message #1 Posted by Thomas Klemm on, 5:43 p.m. Computing Square Roots The Museum of HP Calculators ![]()
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