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 "UB". Indeed, take "B" = "T" to be the unique non-negative square root of "T". If "T" is strictly positive, then "B" is invertible, and so is unitary: If "T" is non-negative without being strictly positive, then the inverse of "B" cannot be defined, but the Moore–Penrose pseudoinverse "B" can be. In that case, the operator is a partial isometry, that is, a unitary operator from the range of "T" to itself. This can then be extended to a unitary operator "U" on the whole space by setting it equal to the identity on the kernel of "T". More generally,