Answered Essay: The Babylonian algorithm to compute the square root of a number n is

Dear Student,

here i have written the C++ program as per the requirement.I have also inclueded the comment for better understanding.

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Note: Please note that the below program has been tested on ubuntu 16.04 system and compiled under g++ compiler. This code will also work on other IDE’s and C++ microsoft visual studio express.

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Program:

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//Header file declration

#include <iostream>

#include<stdlib.h>

//Namespace declration

using namespace std;

int main()
{

//variable data type declration

double n, count = 0;

double answer, guess, r;

//input a double number

cout << “Please enter a double number: “;

cin >> n;

//input a guess

cout << “Please enter a ‘guess’ number to divide by double number: “;

cin >> guess;

//assign the guess to a new variable previous_guess
double previous_guess = guess;

double new_guess;

int new_count;

//loop until the guess is less than the 1% of the previous guess

while(count<100)
{

r = n/previous_guess;

new_guess = (previous_guess + r)/2;

//when guess is less than the 1% of the previous guess
//break the loop
if((new_guess – previous_guess) < (previous_guess * 0.01))

{

new_count = count;

answer = new_guess;

break;

}

//else execute this condition

else

{

r = n/new_guess;

previous_guess = (new_guess + r)/2;

}

//increment count

count++;

}

//display the count

cout<<“guess is within 1% of the previous guess. in “<< new_count<<” counts”<<endl;

//display the squre root

cout << “The sqaure root of “<< n << ” is ” << answer;

cout << endl;

return 0;

}//end of the main function

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here i have attached the output of the program as a screen shot…

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Output:

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