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 Conversely, it is trivially true that every operator of the form "B* B" is non-negative. Therefore, an operator "T" is non-negative if and only if "T" = "B* B" for some "B" (equivalently, "T" = "CC*" for some "C"). The Cholesky factorization provides another particular example of square root, which should not be confused with the unique non-negative square root. If "T" is a non-negative operator on a finite-dimensional Hilbert space, then all square roots of "T" are related by unitary transformations. More precisely, if "T" = "A*A" = "B*B", then there exists a unitary "U" such that "A" =