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 shown to contain no solutions as follows. Since formula_24 is even, formula_29 must be divisible by formula_30, which makes the entire equation congruent to modulo formula_30: The square of any odd number is always formula_33. The square of any even number is always formula_34. Since both formula_18 and formula_19 are odd and formula_24 is even, we have: which is impossible. Therefore, the fifth possibility is also ruled out, leaving the sixth to be the only possible combination to contain solutions, if any. An extension of this lemma is the result that two identical whole-number squares can never be added to