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Need to find one billion decimal places when taking the root of 5?
While there is no idea, you need at least an idea
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Something like this stackoverflow.com/questions/15362117/find-as-many-...
Apparently according to Newton's method , only you still need to use some library to work with large numbers.
There is a CORDIC method , it belongs to the "digit by digit" methods and allows you to get one next digit at each iteration to calculate various functions, including roots (in the sense of fractional powers of a number).
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