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How many ways does anyone know to obtain the square root of a number? I will list those that I know. I would like to know if there are any others. I don’t know of any that were introduced in the twenty-first century. Can anyone list any other methods?
In approximate order of date of introduction:
a. Use a pencil-and-paper procedure that resembles a more complicated version of long division.
b. Use logarithms.
c. Use an iterative method, such as Newton’s method. These are methods for successive numerical approximation of the solution to any of various equations that cannot be exactly solved by algebra. (This probably would not have been actually done in the eighteenth century, because for square root, it involves more steps than long division.)
d. Use a table of square roots. Interpolate if necessary. The generation of the table of square roots was done using either long division or logarithms. (It wouldn’t have been done by iteration, because for square root, that takes longer than long division.)
e. Use a slide rule.
f. Write a computer program that computes square roots. (The program will probably either use logarithms or implement an iterative method.)
g. Use a calculator. (The calculator may rely on logarithms, but that is only my guess, because I haven’t seen the hardware logic of a calculator.)
h. Use Excel. (Excel probably relies on logarithms. That is only my guess, because I haven’t seen the source code of Excel).
Any other ideas?
Robert McClenon (talk) 15:52, 9 December 2014 (UTC)