Newton's method for approximating square roots.

root.cpp

/*
 * Testing a simple square-root method.
 *
 * g++ -std=c++11 -Wall -Werror -Wextra -pedantic -pedantic-errors root.cpp -o root
 */

#include <iostream>

static constexpr double EPSILON = 1.0e-9;

template <typename num_t>
num_t root(num_t n, num_t precision = EPSILON) {
    if (n == num_t{0}) {
        return num_t{0};
    }

    num_t guess = n / num_t{3};

    while (true) {
        const num_t lastGuess = guess;
        guess = (guess + (n/guess)) / num_t{2};

        if (std::abs(lastGuess-guess) <= precision) {
            break;
        }
    }

    return guess;
}

int main() {
    std::cout << "Sqrt 49:  " << root(49) << std::endl;
    std::cout << "Sqrt 36:  " << root(36) << std::endl;
    std::cout << "Sqrt 100: " << root(100) << std::endl;

    return 0;
}