Step by Step solution about How to resolve the algorithm Nth root step by step in the JavaScript programming language

The provided JavaScript function, nthRoot, calculates the nth root of a given number num using the Newton-Raphson method with a specified precision prec (defaulting to 12). Here's a detailed explanation of the code:

1. Function Signature:

   function nthRoot(num, nArg, precArg) {

   The function nthRoot takes three parameters:

   • num: The number for which the nth root is to be calculated.
   • nArg (optional): The value of n, which represents the nth root to be calculated. Defaults to 2, indicating a square root if not provided.
   • precArg (optional): The desired precision of the result. Defaults to 12 decimal places if not provided.

2. Initialization:

   var n = nArg || 2;
   var prec = precArg || 12;

   The variables n and prec are initialized with their respective default values (2 and 12) if not provided as arguments. n represents the nth root to be calculated, and prec determines the number of decimal places to which the result should be accurate.

3. Iteration (Newton-Raphson Method):

   var x = 1; // Initial guess.
   for (var i=0; i<prec; i++) {
    x = 1/n * ((n-1)*x + (num / Math.pow(x, n-1)));
   }

   The code uses the Newton-Raphson method to iteratively refine an initial guess x to converge to the nth root of num. The initial guess x is set to 1.

   Inside the loop, which iterates prec times to achieve the desired precision, the value of x is updated using the Newton-Raphson formula:

   • The first term, 1/n, is a constant factor.
   • The second term, (n-1)*x, involves multiplying the previous value of x by n-1.
   • The third term, (num / Math.pow(x, n-1)), calculates a fraction where num is divided by the previous x raised to the power of n-1.

   The updated value of x is then used in the next iteration of the loop, gradually converging to the nth root of num.

4. Result:

   return x;

   After the loop completes, the function returns the final value of x, which represents the calculated nth root of num with the specified precision.

5. Example Usage: This is an example of how you can use the nthRoot function to calculate the cube root of 27:

   const cubeRoot = nthRoot(27, 3);
   console.log(cubeRoot); // Output: 3

function nthRoot(num, nArg, precArg) {
  var n = nArg || 2;
  var prec = precArg || 12;
  
  var x = 1; // Initial guess.
  for (var i=0; i<prec; i++) {
    x = 1/n * ((n-1)*x + (num / Math.pow(x, n-1)));
  }
  
  return x;
}