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 Integer square root In number theory, the integer square root (isqrt) of a positive integer "n" is the positive integer "m" which is the greatest integer less than or equal to the square root of "n", For example, formula_2 because formula_3 and formula_4. One way of calculating formula_5 and formula_6 is to use Newton's method to find a solution for the equation formula_7, giving the iterative formula The sequence formula_9 converges quadratically to formula_5 as formula_11. It can be proven that if formula_12 is chosen as the initial guess, one can stop as soon as to ensure that formula_14 For