Nth root algorithm: Difference between revisions

Revision as of 00:44, 16 June 2008

Revision as of 10:25, 16 June 2008

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The principal [[nth root|''n''th root]] <math>\sqrt[n]{A}</math> of a [[negative and positive numbers|positive]] [[real number]] ''A'', is the positive real solution of the equation

:<math>x^n = A</math>

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leading to the general ''n''^th root algorithm.

== MANUAL NTH ROOT APPROXIMATION METHOD ==

Approximation of the nth root of a positive number may be done with the following method:

<math>X^1/n = (A+B)^1/n= A^1/n+ B/(n(A^1/n)^n-1</math>

where A is the n expansion of a trial root, which is close to X, and B is the complement of A to complete X.

Example; find the 5th root of 34.

Solution; 2⁵ = 32 hence; 34^1/5 = (32 + 2)^1/5 = 2 + 2/(5x16) = 2 + 0.025 =2.025

The error in the approximation is only about 0.06 %

[[Category:Root-finding algorithms]]