Newton’s method is a method for finding approximations to the roots of a given function.

The method itself is very simple, you give an initial guess of the root, \(x_0\), and calculate further values using the following equation: \(x_{n+1}=x_n-\frac{f’(x_n)}{f(x_n)}\).
Generally, each term in the sequence is more accurate in comparison to the previous terms.

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A few days ago I thought of an algorithm to calculate square roots. In this article I would like to introduce my algorithm.
I should mention that this algorithm probably exists.

First of all, my algorithm can only find roots between a specific range (for example \(0\) to \(1\)), thus we need to decrease [...]