How to resolve the algorithm Nth root step by step in the Racket programming language

Published on 12 May 2024 09:40 PM
#Racket

How to resolve the algorithm Nth root step by step in the Racket programming language

Table of Contents

Problem Statement

Implement the algorithm to compute the principal   nth   root

A

n

{\displaystyle {\sqrt[{n}]{A}}}

of a positive real number   A,   as explained at the   Wikipedia page.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Nth root step by step in the Racket programming language

Source code in the racket programming language

#lang racket

(define (nth-root number root (tolerance 0.001))
  (define (acceptable? next current)
    (< (abs (- next current)) tolerance))
  
  (define (improve current)
    (/ (+ (* (- root 1) current) (/ number (expt current (- root 1)))) root))
  
  (define (loop current)
    (define next-guess (improve current))
    (if (acceptable? next-guess current)
        next-guess
        (loop next-guess)))
  (loop 1.0))

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