C# version of Newton Raphson Method. Go : https://gist.github.com/guitarrapc/bdf51e61d50ad3e70b3bb2290797b5fe

Main.cs

void Main()
{
    double input = 67000000000;
    var result = Sqrt(input);
    Console.WriteLine($"try: {result}");
    Console.WriteLine($"math: {Math.Sqrt(input)}");
}

// input: 67000000000
// count: 24
// try: 258843.582110896
// math: 258843.582110896

double Sqrt(double x)
{
    double prev,z = 1.0;
    var i = 0;
    var init = false;
    const double threshold = 0.00000000001;
    while (true)
    {
        i++;
        prev = z;
        z -= (z * z - x ) / (2 * z);
        if (z == prev || (init && Math.Abs(prev) < Math.Abs(z + threshold)))
            break;
        init = true;
    }

    Console.WriteLine($"input: {x}");
    Console.WriteLine($"count: {i}");
    return z;
}