Newton's method for finding nth root of number r to p decimal places correct

roots.py

def newton(n, r, p = 0):
    """
    (int(n), num(r), int(p)) -> float
    Return the nth root of a positive number r displaying p correct decimals.
    """

    x = 1  # start with guess = 1

    while True:
        fx = x**n - r  # function of this form solves all roots
        fdx = n * x**(n - 1)
        x_n = x - (fx / fdx)
        if abs(x_n - x) < 10**(-p):  # checks consecutive difference
            return round(x_n, p + 1)  # show 1 extra decimal for rounding error
        x = x_n 

if __name__ == '__main__':
    n = int(input("Which root to take: "))
    r = float(input("Which number to root: "))
    p = input("Decimal correct to: ")
    if not p.isdigit():  # check if valid p is entered
      p = 0
    print(newton(n, r, int(p)))  # p as str cast into int