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François Viète's On the Numerical Resolution of Powers by Exegetics published in 1610 (Viete, 2006, pp. 311-370) introduced one way of numerically solving polynomial equations, a special case of which is the equation where the square of an unknown is equal to a given number. Thomas Harriot's The Practice of the Analytic Art (Harriot, 1631) built upon Viète's work.

It seems that Viète's and Harriot's procedure is the basis of the manual decimal digit-by-digit method of obtaining square roots (as seen in Wikipedia, 2014).

I was taught this procedure when I was in elementary school. My question is:

When was the manual decimal digit-by-digit method of obtaining square roots first taught to school children?

I'm looking for evidence such as a textbook containing the procedure and explicitly stating that children (say, those below 18 years of age) are the intended audience.

References:

Harriot, T. (1631). Artis analyticae praxis, ad aequationes algebraicas noua, expedia, & generali methodo, resoluendas : tractatus. Londini: Barker. Retrieved January 29, 2014, from http://echo.mpiwg-berlin.mpg.de/MPIWG:DBZ6XPZN

Viète, F. (2006). The anayltic art: Nine studies in algebra, geometry and trigonometry from the opus restitutae mathematicae analyseos, seu algebrâ novâ (T. R. Witmer, Trans.). Mineola, New York: Dover Publications.

Wikipedia. (2014). Methods of computing square roots---Wikipedia, the free encyclopedia. Retrieved January 29, 2014, from http://en.wikipedia.org/w/index.php?title=Methods_of_computing_square_roots&oldid=589727868

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    $\begingroup$ Upvoted for all those references. $\endgroup$
    – Tom Au
    Oct 29 '14 at 19:31
  • $\begingroup$ May I ask when and where you went to elementary school, and if it was a public or private school? A good place to start the research might be to look into the origin of the math curriculum in that country at that time (although I suspect that could be hard to track down depending on the country). $\endgroup$
    – Jack M
    Nov 28 '14 at 22:12
  • $\begingroup$ @JackM, thanks for the suggestion. I was taught this method around 1985 in a private elementary school in the Philippines but I suspect that the practice started much earlier, perhaps a century or two earlier. I admit I haven't searched systematically yet. $\endgroup$
    – Joel Reyes Noche
    Nov 28 '14 at 22:44
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    $\begingroup$ One place to begin looking for such books in English is the following 19th century restricted google-books search for arithmetic "square root". I read the prefaces of several of these books just now, and my guess is that square root computation was probably not taught before high school in the 1800s. Note that "high school" back then was probably like graduate school today, relative to the percentage of the population involved. $\endgroup$
    – Dave L Renfro
    May 19 '15 at 16:34
  • $\begingroup$ @DaveLRenfro, Although it is not an exact answer to the question, you provided what I was looking for. If you write your comment as an answer, I will accept it until a better answer comes along in the future. Thanks. $\endgroup$
    – Joel Reyes Noche
    May 20 '15 at 0:38
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An early example is

Arithmetick Made fo Easy, That it may be Learned without a Master: After a new and concife method; the Like not yet Extant

The linked second edition was published in 1740. The first edition was 1727. (1725 for the original French: L'arithmétique rendue facile de façon à la pouvoir apprendre sans Maître)

The translator's preface explains it is for teaching children.

Calculating square roots digit by digit is pages 347-350.

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