C# Find Nth Root

Question

I use below method to calculate Nth Root of double value, but it takes a lot of time for calculating the 240th root. I found out about Newton method, but was not able to implement it into a method. Any help would be appreciated.

static double NthRoot(double A, int N)
{
   double epsilon = 0.00001d;//
   double n = N;
   double x = A / n;
   while (Math.Abs(A-Power(x,N)) > epsilon)
   {
    x = (1.0d/n) * ((n-1)*x + (A/(Power(x, N-1))));
   }
   return x;
}

Answer 1

static double NthRoot(double A, int N)
{
    return Math.Pow(A, 1.0 / N);
}

From Wikipedia:

In calculus, roots are treated as special cases of exponentiation, where the exponent is a fraction:

\sqrt[n]{x} \,=\, x^{1/n} 

Answer 2

You can use the same function used to find the power of a number, just use reciprocal of the number instead of the number itself.

To find N root of X you can write,

int root = Convert.ToInt32(Math.Pow(X, (1 / N));