C++ programming (beginner)

The problem of computing the square root of any number is a specific case of the more general root-finding problem. Root-finding occurs in many places in computer science, as well as in other science and engineering problems. Recall that the roots (or zeros) of any function are the parametric value(s) for which the function produces a zero result: x:f(x) 0 Finding the square root of some number Kis equivalent to finding the principal zero of f(x)x- We could just as easily compute the cube root of Kin the same fashion by solving and so on. Generalizing, we can find the n root of any value Kby solving The Newton-Raphson algorithm is an efficient and ingenious method for finding the principal root of any continuously differentiable function. The method is ascribed to Sir Isaac Newton, although Joseph Raphson was the first to publish it in a more refined form. The method is a generalized version of the Babylonian guess and check" approach that you explored in a previous lab. The method generalizes the Babylonian approach by employing the derivative of the function. Given an old guess, x, the new ("better") guess, xi is computed by: f(ai) Note that the Babylonian Algorithm is simply the specific case of Newton-Raphson for f(x-x. K. For the generalized nth root problem, f(x) is: and the derivative, f(x) is: Substituting these formulas, the Newton-Raphson update rule for computing the root of any value K is