The most either side have made to win in the fourth innings of an Ashes Test was Australia's 404 for three at Headingley back in 1948 when Arthur Morris scored 182 and Donald Bradman, widely regarded as cricket's greatest batsman, an unbeaten 173.
If Australia -- who have two days to get the runs albeit on a pitch of increasingly variable bounce -- succeed it will be the third-highest fourth innings total to win any Test and highest in England.
First-innings century-maker Root and Ian Bell each made valuable scores of 60, with both batsmen facing 89 balls apiece today as England maintained a brisk of run-rate of just above four an over.
Off-spinner Nathan Lyon took four for 75.
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Bell's fifty was a return to form for the experienced batsman after his previous nine Test innings had yielded just 56 runs in total.
England were wobbling at 22 for two when Bell came in after skipper Alastair Cook and Gary Ballance had fallen either side of lunch.
But he reeled off four fours in his first 13 balls faced today including a textbook cover-drive boundary off left-arm paceman Mitchell Starc, who appeared to be struggling with an ankle injury.
Australia captain Michael Clarke brought Lyon into the attack but opener Adam Lyth responded by slog-sweeping his sixth ball for six.
Lyth, looking to establish himself in the England set-up, was out for 37 when, pushing forward to a Lyon delivery that bounced and turned to take his outside edge, he was brilliantly caught left-handed by a diving Clarke at slip.
Root's opening three scoring shots all went for four -- a clip off his pads against Mitchell Johnson followed by a back-foot force and steer to third man off Josh Hazlewood.
Bell, who scored three hundreds during England's 3-0 home Ashes series win two years ago, then completed a 75-ball fifty in which 40 runs came in boundaries.
Ben Stokes chipped in with 42 before Durham team-mate Mark Wood, belying his position at No 10, went down the pitch to drive Lyon for a huge straight six and next ball reverse-swept him for four to give England a lead of exactly 400.