Difference between revisions 405664794 and 405664799 on enwiki

{{DISPLAYTITLE:Shifting ''n''th root algorithm}}
{{unreferenced|date=May 2010}}
The '''shifting ''n''th root algorithm''' is an [[algorithm]] for extracting the [[nth root|''n''th root]] of a positive [[real number]] which proceeds iteratively by shifting in ''n'' [[numerical digit|digits]] of the radicand, starting with the most significant, and produces one digit of the root on each iteration, in (contracted; show full)
## Assign <math>y \leftarrow y'</math> and <math>r \leftarrow r'.</math>
# <math>y</math> is the largest integer such that <math>y^n<x B^k</math>, and <math>y^n+r=x B^k</math>, where <math>k</math> is the number of digits of the radicand after the decimal point that have been consumed (a negative number if the algorithm hasn't reached the decimal point yet).
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putaragesss...!!

==Paper-and-pencil ''n''th roots==
As noted above, this algorithm is similar to long division, and it lends itself to the same notation:

      1.  4   4   2   2   4
     ----------------------
 _ 3/ 3.000 000 000 000 000
(contracted; show full)==External links==
*[http://www.homeschoolmath.net/teaching/sqr-algorithm-why-works.php Why the square root algorithm works] "Home School Math". Also related pages giving examples of the long-division-like pencil and paper method for square roots.

[[Category:Root-finding algorithms]]

[[de:Schriftliches Wurzelziehen]]
[[fr:Algorithme de décalage n-racines]]
[[nl:Worteltrekken]]