Back when I was in high school, I learned something that isn’t known by very many people. I learned the method to manually find a square root in a way that is similar to long division. This method allows you to find each decimal place with certainty. You can solve to as many places after the decimal point as you want.
I've never found this long method in print anywhere. I’ve found other simpler methods to finding a square root, but they usually involve closing in on the square root by continuously rerunning the same method. You are never left with a perfect answer because you can never be sure if the successive decimal places are correct. I’m also not sure which method is used by calculators (on which we all depend for square roots these days, which is the beginning of Asimov’s vision for our world coming true, but that’s a future blog entry).
I have no clue why this long method works. But, in a very small effort to fight the future, I’m going to show the method here, soon.
UPDATE: Here's the link to the long method of finding square roots: http://fcsuper.blogspot.com/2005/05/fighting-future-one-square-root-at.html#comments
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