Joe Root his first golden duck in his ODI career. The 5th ODI was better for Root as he scored a quick 21 before being bowled and also took the wicket of George Bailey. England lost the series 2–1 and Root finished the series with 36 runs and 1 wicket. Root was selected for the 2013-14 Ashes series. He was selected at number 6 for the first Test as Michael Carberry was given the opening batsman role alongside Alastair Cook. Root only managed 2 runs from 7 balls in the first innings before being caught off a Mitchell Johnson delivery. In the
Square root of 2 fraction representation: The convergents formed by truncating this representation form a sequence of fractions that approximate the square root of two to increasing accuracy, and that are described by the Pell numbers (known as side and diameter numbers to the ancient Greeks because of their use in approximating the ratio between the sides and diagonal of a square). The first convergents are: . The convergent differs from by almost exactly and then the next convergent is . The following nested square expressions converge to formula_79: The reciprocal of the square root of two (the square root of ) is a