An Introduction To Programming Through C++ || NPTEL Week-4 Programming Assignment 4.1

In continuation of the topic of computing mathematical functions explored in the lectures, we see another method to find square roots.

Suppose we wish to find the square root of some k > 0. Consider the sequence (a0, a1, a2...)

defined by    

    a0 = k

    an+1 = (an + (k/an))/2 for n >= 0

It can be shown that as n increases, the an converges to the square root of k . Write a program that takes as input a double k, and computes its square root using this method. Compute the value of an till (an - an-1 < 1e-5) and then report an correct to 2 decimal places.

Note: Start writing the program directly from main_program. To print a double x correct to 2 decimal places, use

    cout.precision(2);

    cout << fixed << x << endl;

INPUT

k (2 <= k <= 100, of type double) 

OUTPUT

The square root of k correct to two decimal places

SOLUTION: 

int main()

{

    double k, y, x;

    cin >> k;

    if (k < 2 || k > 100)

    {

        exit(0);

    }

    else

    {

        y = k;

        x = (y + (k / y)) / 2;

        while (y - x >= 0.00001)

        {

            y = x;

            x = (y + (k / y)) / 2;

        }

        cout.precision(2);

        cout << fixed << x << endl;

    }

    return 0;

}