Square root of 2 the square root of two, with a reasonable small denominator, the fraction (≈ 1.4142857) is sometimes used. The sequence in the OEIS gives the numerical value for the square root of two, truncated to 65 decimal places: The Babylonian clay tablet YBC 7289 (c. 1800–1600 BC) gives an approximation of in four sexagesimal figures, , which is accurate to about six decimal digits, and is the closest possible three-place sexagesimal representation of : Another early close approximation is given in ancient Indian mathematical texts, the Sulbasutras (c. 800–200 BC) as follows: "Increase the length [of the side] by its third
Integer square root theoretical advantages. One can prove that formula_30 is the largest possible number for which the stopping criterion ensures formula_32 in the algorithm above. In implementations which use number formats that cannot represent all rational numbers exactly (for example, floating point), a stopping constant less than one should be used to protect against roundoff errors. The traditional pen-and-paper algorithm for computing the square root formula_5 is based on working from higher digit places to lower, and as each new digit pick the largest that will still yield a square formula_34. If stopping after the one's place, the result computed will be