Question 1-Coding (15 points Write a new C++ than one million using Heron\'s Met

Question

Question 1-Coding (15 points Write a new C++ than one million using Heron's Method. Search for "Heron's Method" on the web- there are plenty of good YouTube Videos & code examples out there-be Please explain in your own words how Heron's method actually works. Then compare and contrast Heron's Method with Newton's Method (Session 03, Lab 02) in terms of speed (number of iterations required to obtain desired accuracy) and precision. Which method is more efficient and why? -Herons but why console program to calculate and display the square root of a random integer greater sure to give clear & precise credit if you copy someone's code

Explanation / Answer

Heron's method is an iterative method to find the square root of a number. With each iteration of the Heron's method, the result is normally a more precise approximation.

The formula for Heron's method is:

x[i+1] = (x[i] + N/x[i])*0.5 -- where N is the number whose square root must be determined and x[0] is the initial approximation. ( Here we have considered 'N/2' as the initial approximation)

Newton's method is a method for finding successively better approximations to the roots of a real-valued function. When you apply Newton's method to solve the equation f(x) = (x^2) - r = 0, we get Heron's method. However, Heron's method predates the general Newton method.

In cases where the initial value is not close to the reciprocal square root, the iterations will diverge away from it rather than converge to it while applying Newton's method. In such cases Heron's method is considerd more efficient.

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