An Algorithm to Compute Square Roots of Integers

This Demonstration shows a method of computing the square root of a positive number, in this case a nonsquare integer less than 1000. This method was very popular and taught in schools before the advent of calculators but still retains its usefulness in understanding and practicing algorithmic manipulation.
As the description of the algorithm is largely based on practice, we leave a complete description to the references. We mention only that (1) the red number is the result approximated to a selected number of decimal places and (2) brown numbers are obtained by duplicating the current red number and appending a suitable digit to extend the computation. We separate the digits into pairs, starting from the right. Beginning with the leftmost pair of digits we obtain the current blue numbers by multiplying the current red and brown values and subtracting the result from the old blue value in a manner resembling long division.

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For more information, see square root algorithm.
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