This is a version of Newton's method given in Crandall & Pomerance, "Prime Numbers: A Computational Perspective". The reason you should use this version is that people who know what they're doing have proven that it converges exactly to the floor of the square root, and it's simple so ...
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A simple (but not very fast) method to calculate the square root of X: squareroot(x) if x<0 then Error a = 1 b = x while (abs(a-b)>ErrorMargin) a = (a+b)/2 b = x/a endwhile return a; Example: squareroot(70000) a b 1 70000 35001 2 17502 4 8753 8 4381 16 2199...
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