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
Methods of computing square roots that formula_211 is as small as possible. A completely different method for computing the square root is based on the CORDIC algorithm, which uses only very simple operations (addition, subtraction, with bitshift and table lookup to implement multiplication). The square root of "S" may be obtained as the output formula_197 using the hyperbolic coordinate system in vectoring mode, with the following initialization: Quadratic irrationals (numbers of the form formula_216, where "a", "b" and "c" are integers), and in particular, square roots of integers, have periodic continued fractions. Sometimes what is desired is finding not the numerical value of a square