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 2 by 2 matrix pairs: If "R" is a square root of "M", then –"R" is also a square root of "M", since (–"R")(–"R") = (–1)(–1)("RR") = "R" = "M". Let where "A", "B", "C", and "D" may be real or complex numbers. Furthermore, let "τ = A + D" be the trace of "M", and "δ = AD – BC" be its determinant. Let "s" be such that "s" = "δ", and "t" be such that "t" = "τ" + 2"s". That is, Then, if "t" ≠ 0, a square root of "M" is Indeed, the square of "R" is Note that "R"