/**
 * Approximate the square root of n, to within the specified tolerance,
 * using the Newton-Raphson method. This method takes two arguments:
 * @param Double n The number to be square-rooted
 * @param Double tolerance the error tolerance
 * @return Double result of square root operation
 */
public Double approximateSquareRoot(Double n, Double tolerance)
{
    Double root = n / 2;
    while (Math.abs(root - (n / root)) > tolerance)
    {
        root = 0.5 * (root + (n / root));
    }
    return root;
}

/** * Approximate the square root of n, to within the specified tolerance, * using the Newton-Raphson method. This method takes two arguments: * @param Double n The number to be square-rooted * @param Double tolerance the error tolerance * @return Double result of square root operation */ public Double approximateSquareRoot(Double n, Double tolerance) { Double root = n / 2; while (Math.abs(root - (n / root)) > tolerance) { root = 0.5 * (root + (n / root)); } return root; }