Is there a decimal based way to take roots or exponents?

Asked 3 years, 11 months ago

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We all know about division using decimals and places, you just keep dividing each digit place and move on to the next one.

I was wondering if there was a similar method by which you could manually take a root or exponents where you start with one digit place and move on to the right.

asked Feb 23 '16 at 0:53

Simply Beautiful Art

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$\begingroup$ I'm sure there is one for roots, as I remember seing it in high school. For exponentiation, repeated squaring is easy to do on paper, and you can think of it as being "digit-by-digit" if you work in base two. $\endgroup$ – xyzzyz Feb 23 '16 at 1:02
$\begingroup$ @xyzzyz hm, that is interesting. I have yet to see that done before. I think the squaring in base two is probably very interesting. $\endgroup$ – Simply Beautiful Art Feb 23 '16 at 1:06
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$\begingroup$ google: extract square root with pencil and paper . some results: homeschoolmath.net/teaching/square-root-algorithm.php , mathforum.org/library/drmath/view/52605.html , maa.org/press/periodicals/convergence/… $\endgroup$ – Mirko Feb 23 '16 at 1:07
$\begingroup$ @Mirko Thanks! That pretty much answers my question. $\endgroup$ – Simply Beautiful Art Feb 23 '16 at 1:09
$\begingroup$ you are welcome, note one of the above links is about cube (not square) roots. Here are a couple more links, the second of which shows your question is a duplicate: davdata.nl/math/root.html , math.stackexchange.com/questions/90435/… And one extra link, to Wikipedia (copied from the other MSE question), different methods en.wikipedia.org/wiki/Methods_of_computing_square_roots $\endgroup$ – Mirko Feb 23 '16 at 1:14

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