Potential New Algorithm to Calculate the Cube Root of a Number

Edmond Halley's Meridian image by Robbo-Man

Edmond Halley's Meridian: Image by Robbo-Man

A Long-Division Method to Approximate a Cube Root

Another approach uses a special type of long division to make the first approximation, and is helpful for finding a cube root of a “large” number, ‘n’. Let the symbols {a, b, c…h} represent ordinary decimal digits, and ‘a’ is not zero.

Then let “n = abcdefgh” represent a number, such as ‘12345678’.

Break the number into groups of three digits, starting from the units and moving to higher values: “n = ab,cde,fgh”.

Begin to approximate “n^(1/3)” by guessing the lower bound of the cube root of the leftmost group of digits. In this case, guess at the cube root of “ab”. Subtract the cube of this guess from “ab”, then deal with the remainder ‘r’.

The rest of the process is fairly messy to describe, but Cube Root has a good example.

This method is just as deterministic as long division: a person might make a poor guess at any point, then revise that value up or down. If the cube root is not an integer, you may need to continue calculating as many decimal places of precision as required.

Graph of y equals x cubed, image by Mike DeHaan

Graph of y equals x cubed, image by Mike DeHaan

Possible Outcomes for Nirbhay Singh Nahar and NAHNO

One possible outcome for Mr. Nahar is that a flaw will be found in his NAHNO algorithm. The peer review process finds errors in some of the articles submitted to mathematics journals prior to publication.

Another possibility is that NAHNO does not go so far beyond existing methods as Mr. Nahar believes, at least in some circumstances.

The best outcome, however, certainly is possible: that Nahar’s NAHNO algorithm will indeed prove to be a significant and reliable improvement over existing methods for finding the cube root of a real number.


Prokerala News. Have new formula for cube root, says Agra mathematician. (2012). Accessed February 6, 2012.

Black, P. E. Cube Root. (2009). Dictionary of Algorithms and Data Structures , U.S. National Institute of Standards and Technology. Accessed February 6, 2012.

Mathews, J. H. Module for Newton’s Method, and Halley’s Method. California State University at Fullerton (2004). Accessed February 6, 2012.

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© Copyright 2012 Mike DeHaan, All rights Reserved. Written For: Decoded Science
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