Square Root method by subtraction

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Instructions

Returns digits of the float, not the float itself (ie. no decimal points).

Doesn't work with numbers whose square is an integer (9, 16, 25...)

Can accept float (non-whole-number) inputs.

No variables are used.

You can configure the precision inside (default = 15).

Notes and Credits

http://www.afjarvis.staff.shef.ac.uk/maths/jarvisspec02.pdf

Initial step:

Let a = 5n (this multiplication by 5 is the only time when an operation other than addition and subtraction is involved!), and put b = 5.

Repeated steps:

(R1) If a ≥ b, replace a with a − b, and add 10 to b.

(R2) If a < b, add two zeroes to the end of a, and add a zero to b just before the final digit (which will always be ‘5’).

Conclusion:

Then the digits of b approach more and more closely the digits of the square root of n.

Shared: 13 Sep 2016 Modified: 21 Dec 2016
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