Out of curiosity, this calculator implements nth root algorithm. This is iterative algorithm which is said to be very fast-converging, so the calculator lists the results of each iteration: current computed root value and current delta from previously computed root value. Calculator stops the iterations when desired precision is obtained, in other words, when the delta between previous and current computed roots is less than a precision. The description of the algorithm can be found below the calculator.
nth root algorithm
The algorithm is quite simple.
Step 1. Make an initial guess
In this calculator to get initial guess I simply divide number by root's degree if number is more than 1, and multiply by root's degree otherwise.
Step 2. Set
For precision check, it is more practical to compute delta separately
Step 3. Repeat step 2 until the desired precision is reached:
The algorithm can be derived from Newton's method for
where x is the root, and A is positive real number.