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Message: [QUOTE="Gavin Sinclair, post: 4653066"] There's an algorithm for calculating square roots, similar (in appearance, not in process) to the algorithm for long division. One or more generations ago, school students would have done it with pen and paper, I think. Furthermore, there's a Calculus-based algorithm (Newton's method, it's called in my syllabus, but I think it's properly called the Newton- Raphson method) for calculating square/cube/fourth/... roots to any desired accuracy. Thirdly, you can estimate any root you like by trial multiplication! (Exercise: write a Ruby program to do this; shouldn't take more than 10 lines.) [/QUOTE]