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July 6

How do I say the Nth root of a number?

I asked this question in the linguistic desk. But the math desk is probably a much better place for this question. How do I say:

${\sqrt[{n}]{a}}$

when n equals to -3, -2, -1, 1.5, or 2.5? - Toytoy (talk) 05:19, 6 July 2021 (UTC)[reply]

I think it's better to answer at ref desk lang to avoid dispersion/fragmentation (It also isn't really a math question and I meant "soon" as a couple of days, but that's nitpicking). Personuser (talk) 06:13, 6 July 2021 (UTC)[reply]

You would normally only say "nth root" when n is an integer >3. n=2 would be square root and n=3 would be cube root. For n=-3 you'd say

n^{-1/3}

and so forth. 2602:24A:DE47:BA60:8FCB:EA4E:7FBD:4814 (talk) 08:09, 6 July 2021 (UTC)[reply]

The question has a simple answer: you don't say anything because you don't use that notation in those cases, instead you write fractional powers. (I note that you have received two different versions of this correct answer already at the language desk; maybe third time's a charm?) --JBL (talk) 11:18, 7 July 2021 (UTC)[reply]

Bitcoin mining

Do the calculations have any real-world, non-Bitcoin value? Clarityfiend (talk) 05:23, 6 July 2021 (UTC)[reply]

No not really. 2602:24A:DE47:BA60:8FCB:EA4E:7FBD:4814 (talk) 08:10, 6 July 2021 (UTC)[reply]

(Real-world questions are probably not mathematical in nature.) Value to whom? If you succeed in mining a coin, you may turn your proof of work into an NFT and auction it off :). Simpler, you may exchange the coin for fiat money using a service such as Binance. But then, one may ask, does fiat money have any real-world, non-money value? Your "money" is probably a bunch of bits in a file on a server of some bank. --Lambiam 08:13, 6 July 2021 (UTC)[reply]

Not Bitcoin, but some other cryptocurrencies such as Primecoin have attempted to make theirs somewhat useful. --116.86.4.41 (talk) 10:08, 6 July 2021 (UTC)[reply]

Thanks. Now that I think about it, it should have gone to the Computing Refdesk. Clarityfiend (talk) 11:51, 11 July 2021 (UTC)[reply]