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Код

public class Sqrt {

    public double epsilon = 0.0000001; // tochnost' vychislenij

    public static void main(String[] args) {
        double result = new Sqrt().sqrt(10.0);

        System.out.println((result));
    }

    /*
    // iterations - tochnost' vychislenija..
    public double sqrt(final double x, final int iterations) {
        if (x <= 0) {
            return .0;
        } // zdes' po vkusu..

        double result = .4;
        for (int ii = 0; ii < iterations; ii++) {
            System.out.println(result);
            result = (result + x / result) / 2;
        }
        return result;
    }
    */

    public double sqrt(double x) {
        double sq = x;

        while (doubleabs(sq * sq - x) >= epsilon) {
            sq = 0.5 * (sq + x / sq);
        }
        return sq;
    }

    double doubleabs(double x) {
        if (x < 0) {
            return -x;
        } else {
            return x;
        }
    }

}