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The mathematical formula for calculating the square root of a number is x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}=x_n-\frac{x_n^2-S}{2x_n}=\frac{1}{2}\left(x_n+\frac{S}{x_n}\right).

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Q: What is the mathematical formula for calculating the square root of a number?
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