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I do know how to like get root 2 but it's the long division method, and from just seeing it I am genuinely confused how they would implement it. Then there is the prime factorization method but it doesn't get it for irrationals. I do understand for pi though, it maybe predefined but how is it done for other irrationals?

Tejas Agrawal
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    https://en.wikipedia.org/wiki/Methods_of_computing_square_roots – JMoravitz Jan 03 '24 at 15:33
  • Hi try adding what you have tried in the problem as it is needed for the site guidelines – Fran Aguayo Jan 03 '24 at 15:48
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    A computer is unable to deal with infinitely many digits, so the concept of irrational is not very useful in this context. However, the answer may depend on what kind of computation you mean: floating-point as supported by the CPU (e.g. 64 bits, and a 52-bit mantissa), and the square root is either implemented in hardware, or as a numerical library - or multiprecision as done by specialized software (e.g. the mpfr library, or computer algebra systems). – Jean-Claude Arbaut Jan 03 '24 at 16:18
  • closely related to https://math.stackexchange.com/q/1295373/925076 – Dheeraj Gujrathi Jan 03 '24 at 16:33
  • Or https://math.stackexchange.com/questions/1733165/how-are-the-digits-of-an-irrational-number-computed?rq=1 – Dan Jan 03 '24 at 17:45

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