Implement a Python program that calculates the $n^{th}$ root of a given positive number using Newton's method. Define a function recursive root that takes numbers $x$ and $n,$ and a precision parameter $(lon{)}_4$ and returns the $n^{th}$ root of $x$ using recursion. Prompt the user to input a number $x$ and $n,$ and display the result using the function. Take $x=81$ and $n=4,$ and compare the output of your function with math.pow $(x,\frac{1}{n}).$

To find the $n^{th}$ root of a number $x$ using newton method, start with a first guess $)=(\frac{x}{n},$ then update $u$ using the following formula:

$u=u-\{\begin{array}{c}\text{:}[u^n-x]\\ n^{n-1}\end{array}$

Until $|u^n-x|lon$

Solution: