just to add to the conversation ... once one learns algebra and expresses a number as polynomial of 10, one can just derive the usual manual algorithm for any i

just to add to the conversation ... once one learns algebra and expresses a number as polynomial of 10, one can just derive the usual manual algorithm for any integer root ... though it gets tedious very quickly with hisgher roots ... in addition to methods using Taylor expansion and such ... maybe this is a reason why there is no need to teach it ... apart from the practical reason of a calculator can do it much quicker ...