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.
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