# What is the history of $\sqrt{}$

Why we use the symbol $\sqrt{}$ when we take square roots ? Anybody knows the history ?

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vote up. History is important and things like this must be taught in high schools. –  user30338 Jan 16 '13 at 13:05
This was already asked and answered at Mathematics StackExchange: math.stackexchange.com/questions/15787/how-did-the-square-root-get-its-shape/ –  Joel Reyes Noche Jan 16 '13 at 13:17
@Berlusconi: everything? Try to fit a fraction in your square root. (Please, do not take my comment as an invitation to post another version with enough phantoms to make it taller. We all know how the symbol looks like.) –  Emil Jeřábek Jan 16 '13 at 14:08

We use "\sqrt" (in TeX) since Knuth chose that command for the square root symbol.

Square roots have been computed since the days of the Babyloneans, but they didn't use the symbol.

The symbol √ for the square root was first used in print in 1525 in Christoph Rudolff's Coss.

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The last sentence seems a little harsh. The question itself seems perfectly reasonable to me (even if the answer is not difficult to find). @Rita: there is more information at jeff560.tripod.com/operation.html. –  Todd Trimble Jan 16 '13 at 13:05
Tangential but: I doubt the information regarding + and - is correct. (Indeed, one of the links you give agrees with me.) –  quid Jan 16 '13 at 13:11
@Uwe: history of mathematics questions are generally honored here, but with some caveats (which are hard to summarize, but some involve the feasibility of obtaining definitive answers); they are best judged on a case-by-case basis. It should be recognized, though, that such questions commonly arise in mathematics research, as when one is trying to write historical notes in research monographs. –  Todd Trimble Jan 16 '13 at 13:39
@Trimble: Thanks for the explanation, I myself didn't mind the question, otherwise I would not have answered it. But I had the feeling that I have seen similar questions getting closed quite fast. –  Uwe Franz Jan 16 '13 at 14:06
Oh, you are talking about the name of the command rather than the actual symbol? That’s not what the OP asked, but anyway, I don’t think that the answer to that question is correct either: sqrt is a name commonly given to the square root function in various programming languages (notably including Pascal, in which TeX was written), and Knuth just followed suit. –  Emil Jeřábek Jan 16 '13 at 15:02

This question has already been completely answered, but here is a bit more on history.

The symbol has its origin in the Latin letter R as an abbreviation of radix (latin: root). It has been used by Leonardo de Pisa (Fibonacci) in his seminal book Liber Abaci (1202) where he treats square roots and cubic roots in chapter 14 and 15 (as well as in his later less well known Liber Quadratorum (1225)).

Fibonacci, like Euclid, did not invent all the mathematics he reports, but took much of it from the Arabian world, mainly from al-Khwarizmi and Omar Khayyam. The Arabian word for "root" had been used by al-Khwarizmi already; his word is rendered radix in translations from the Arabic to Latin by Robert of Chester, John of Seville, and Gerard of Cremona. It appears also in Alexandre de Villedieu's Carmen de Algorismo (1240) and in Sacrobosco's Algorismus (1250). By the way Fibonacci calculates approximations but considers roots as exact numbers, even if they cannot be expressed as integers or fractions.

Following the tradition of medieval writers, Nicolas Chuquet used the uppercase Latin letter R with a small stroke, looking very similar to Px when written close together. Both, R and R$^2$ indicate the square root, R$^3$ indicates the cubic root, R$^4$ the forth root and so on. Regiomontanus (1464), Luca Pacioli (1494), and Estienne de la Roche (1520) adopted this sign.

The hook-like symbol √ that resembles a small r was introduced by Christoff Rudolff in his book "Die Coß" (1525), the first German book on algebra. He used c√ for cubic root and √√ for fourths root. (By the way he introduced also the convention $x^0$ = 1). English, French and Italien writers were slow in adopting that German sign. Even in Germany the symbol "l" for latus (side of the square) was long in use. After Michael Stifel had published the second edition of Rudolff's Coß (1553) the symbol became more and more accepted.

René Descartes (1596 bis 1650) invented (or extended) the bar above the radicand (this word being first used in 1889) in order to indicate what symbols belong to the radicand.

Moritz Cantor: "Vorlesungen über Geschichte der Mathematik", Teubner, Leipzig (1894) http://archive.org/stream/vorlesungenber02cantuoft#page/n5/mode/2up

Florian Cajori: "A History of Mathematics" MacMillan, London (1909) http://www.gutenberg.org/files/31061/31061-pdf.pdf

David Eugene Smith: "History of Mathematics, vol. 2", Dover Publications (1958) http://books.google.de/books/about/History_of_Mathematics.html?id=uTytJGnTf1kC&redir_esc=y

http://jeff560.tripod.com/r.html

http://www-history.mcs.st-and.ac.uk/Biographies/Fibonacci.html

Edit As Paul Taylor said Florian Cajori favours another root of the root symbol, namely the generation of an upstroke from a row of points. In fact there may have been many sources playing together. Moritz Cantor points out that Alkasadi (or Alkasawi) an Arab living in Spain (died 1477 or 1486) wrote a book which is known under different titles like Lifting the veils of the science of the Gubar (Gubar means "dust" or "calculating with digits") where he not only abbreviated the Arab word for root dschidr by writing its first letter, but wrote it not right of the radicand (in Arabic, meaning in front of the radicand) but above. The jim can be seen in the column Initial in the table Arabic letters usage in Literary Arabic. This could also be a source for our root symbol.

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One more reference: this question, and its resolution in the resemblance to a small "r" (for "radix"), is also brought up in Barry Mazur's Imagining numbers (particularly the square root of minus fifteen), where further historical references may be found. –  Vesselin Dimitrov Feb 8 '13 at 17:20
Thank you for the hint. And for those too lazy to lift a real book to the eyes here you can catch a glimpse: amazon.com/Imagining-Numbers-particularly-square-fifteen/dp/… –  Rhett Butler Feb 8 '13 at 19:16
As well as his "narrative" History of Mathematics, Florian Cajori wrote a History of Mathematical Notation in two volumes that reports on the examination of a large number of manuscripts. In this, he denies the obvious derivation of the symbol from an "r". He says that, along with the crossed R notation, it was also customary to write roots using dots. Bizarrely, one dot was a square root, two a fourth, three a cube and four a ninth! Somehow this dot acquired an up-stroke, and that became the modern root symbol. –  Paul Taylor Apr 24 '13 at 5:45