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 p. 18). This proof constructively exhibits a discrepancy between and any rational. "Proof": For the given equation, there are only six possible combinations of oddness and evenness for whole-number values of formula_18 and formula_19 that produce a whole-number value for formula_24. A simple enumeration of all six possibilities shows why four of these six are impossible. Of the two remaining possibilities, one can be proven to not contain any solutions using modular arithmetic, leaving the sole remaining possibility as the only one to contain solutions, if any. The fifth possibility (both formula_18 and formula_19 odd and formula_24 even) can be