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

The provided Ruby code defines a method called nthroot that calculates the nth root of a given number a using a Newton-Raphson iteration method.

Method Signature:

• def nthroot(n, a, precision = 1e-5)

Parameters:

• n: The root to be calculated (e.g., for square root, n is 2).
• a: The number for which the root is to be calculated.
• precision: (Optional) A precision threshold. The method iterates until the difference between the current and previous estimates falls below this threshold.

Implementation:

1. It initializes the iteration with an initial guess x set to the value of a.

2. It enters a loop that iteratively updates x. In each iteration:

   • It calculates the next estimate of the root using the formula: ((n - 1) * prev + a / (prev ** (n - 1))) / n.
   • It updates prev with the previous value of x.

3. The loop continues until the absolute difference between the current x and the previous prev becomes less than the specified precision threshold. This indicates that the root estimate has reached the desired level of accuracy.

4. Finally, the method returns the calculated nth root of a.

Example:

In the given example:

• nthroot(5, 34) calculates the 5th root of 34.
• The result is approximately 2.02439745849989, which is a reasonable approximation of the 5th root of 34.

def nthroot(n, a, precision = 1e-5)
  x = Float(a)
  begin
    prev = x
    x = ((n - 1) * prev + a / (prev ** (n - 1))) / n
  end while (prev - x).abs > precision
  x 
end

p nthroot(5,34)  # => 2.02439745849989