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
Square root of a matrix is an "n" × "n" complex matrix "ρ" that is positive semidefinite with trace 1. If "ρ" can be expressed as where formula_36 and ∑ "p" = 1, the set is said to be an ensemble that describes the mixed state "ρ". Notice {"v"} is not required to be orthogonal. Different ensembles describing the state "ρ" are related by unitary operators, via the square roots of "ρ". For instance, suppose The trace 1 condition means Let and "v" be the normalized "a". We see that gives the mixed state "ρ". In the Unscented Kalman Filter (UKF), the square root of