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 to converge. In linear algebra and operator theory, given a bounded positive semidefinite operator (a non-negative operator) "T" on a complex Hilbert space, "B" is a square root of "T" if "T" = "B* B", where "B*" denotes the Hermitian adjoint of "B". According to the spectral theorem, the continuous functional calculus can be applied to obtain an operator "T" such that "T" is itself positive and ("T") = "T". The operator "T" is the unique non-negative square root of "T". A bounded non-negative operator on a complex Hilbert space is self adjoint by definition. So "T" = ("T")* "T".