Online Tool for Approximating the n-th Root
This algorithm provides an approximate solution for computing the n-th root of a number. Simply specify the root index, the radicand, an initial estimate, and the acceptable error margin (tolerance).
Compute the n-th root of N
This algorithm is based on the generalized Newton’s method: \[ x_{k+1} = \frac{1}{n} \cdot \left( (n - 1) \cdot x_k + \frac{A}{x_k^{n - 1}} \right) \] Where:
- \( x_k \) is the current approximation
- \( x_{k+1} \) is the next approximation
- \( A \) is the number whose n-th root is being calculated
- \( n \) is the degree of the root
For a detailed explanation of the algorithm, see this page.
