Difference between revisions 628323016 and 628323133 on enwiki

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Shifting nth root algorithm
{{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)            1 73 20 25 = 20×17320×5+5^2
            ----------
               2 79 75

===Cube root of 5===
      1.  7   0   9   9   7
     ----------------------
 _ 3/ 5.
⏎
⏎
 000 000 000 000 000
  \/  1 = 300×(0^2)×1+30×0×(1^2)+1^3
      -
      4 000
      3 913 = 300×(1^2)×7+30×1×(7^2)+7^3
      -----
         87 000
              0 = 300×(17^2)*0+30×17×(0^2)+0^3
(contracted; show full)          ----------------------   40×16265×(7^3)+7^4
           1 1295 2830 2447 6799

==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]]
[[Category:Computer arithmetic algorithms]]