I recently saw a title of a video about how to find the square root of 2000. Having taught the math background for solving problems like this for our computer, and actuarial students, I was happy to try this problem, without watching the video. The easiest thing in the world is to type in 2000 into a calculator, and then press the Square Root key, and we would get the square root in one shot. But that would be no fun to us math people; we would prefer to have some more meaty mathematics to sink our teeth into!
Finding square roots directly is a skill that is slowly vanishing. It isn't something that we teach youngsters in school, to do with paper and pencil; over the years, math teachers have never been coached with this method in their school years either, so they don't even know that there is a direct method. Everyone relies on calculators to do it for them; in fact there's hardly any reason to actually find square roots anymore in this brave new world. Approximations, though, could still be useful, especially polynomial approximations.
[I don't really know why I put this post in this blog! The topic of 'Approximation with sines and cosines' might have made a little sense, because of the harmonic series, and so on ... Some of my best buddies are dead; they might be messing with my head ... Anyway, it's probably time to move it 'next door', into I Could Be Wrong, But ...]
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