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You can try using taylor series to calculate more precise square roots.
https://www.sololearn.com/discuss/292240/?ref=app
The math remains the same.
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You can read the formula from here : https://www.mathsisfun.com/algebra/taylor-series.html
The derivative of √x is 1/(2√x)
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Here is a better process, without derivatives : burningmath.blogspot.com/2013/12/finding-square-roots-of-numbers-that.html?m=1
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you can always use the newton method:
https://en.m.wikipedia.org/wiki/Newton%27s_method