Regarding sqr root of 7720.17: I enjoyed your graphical presentation but I’m lazy I suppose. I tried my old fashion iterative method — -I looked at the first two digits (77) and thought 8x8=64, so 80 x 80=6400. Upping to 85 x 85=7225, 88 x 88=7744, which gets me close enough to add some precision. Not pretty but would be good for what I usually require. :=)
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