History
The Yale Babylonian Collection YBC 7289 clay tablet was created between 1800 BC and 1600 BC, showing and as 1;24,51,10 and 42;25,35 base 60 numbers on a square crossed by two diagonals.
The Rhind Mathematical Papyrus is a copy from 1650 BC of an even earlier work and shows how the Egyptians extracted square roots.
In Ancient India, the knowledge of theoretical and applied aspects of square and square root was at least as old as the Sulba Sutras, dated around 800–500 BC (possibly much earlier). A method for finding very good approximations to the square roots of 2 and 3 are given in the Baudhayana Sulba Sutra. Aryabhata in the Aryabhatiya (section 2.4), has given a method for finding the square root of numbers having many digits.
In the Chinese mathematical work Writings on Reckoning, written between 202 BC and 186 BC during the early Han Dynasty, the square root is approximated by using an "excess and deficiency" method, which says to "...combine the excess and deficiency as the divisor; (taking) the deficiency numerator multiplied by the excess denominator and the excess numerator times the deficiency denominator, combine them as the dividend."
A symbol for square roots, written as an elaborate R, was invented by Regiomontanus (1436 - 1476). An R was also used for Radix to indicate square roots in Giralamo Cardano's Ars Magna.
According to historian of mathematics D.E. Smith, Aryabhata's method for finding the square root was first introduced in Europe by Cataneo in 1546.
The symbol √ for the square root was first used in print in 1525 in Christoph Rudolff's Coss, which was also the first to use the then-new signs '+' and '−'.
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