When I was in grade school, before calculators ( showing my age ) we were shown a way of calculating a square root in a way similar to long division. I have forgotten this technique can anyone explain it?
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ANSWERS: 2
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Yes but I prefer to give you a web reference with the algorithm described in a section named "Decimal". http://en.wikipedia.org/wiki/Methods_of_computing_square_roots
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I don't know if this is the method you learned, but with a piece of paper and a little time you could use this method to calculate any square root (and it can be altered for xth route): sqrt(y) = (x + (y/x))/2 Where x is a guess of the square root of y. To find the square root of nine (just as an example because it works out evenly), let's say we guessed 2. We would now do: (2 + (9/2))/2 or (2+4.5)/2 = 6.5/2 = 3.25 Now we would do the same thing, but with 3.25 as x now: (3.25 + (9/3.25))/2 = 3.0096... (3.0096 + (9/3.0096))/2 = 3 The number of times this needs to be repeated depends on the accuracy, for rational square roots, lower accuracy in the division is actually faster. Each time this algorithm is repeated you get a more accurate guess until you eventually get the correct answer, unless the answer is irrational. If you want, I can also explain why it works, but it would take a little while.
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