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

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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