Root, making the most of his early-season time with Yorkshire, started on 92 not out overnight and cruised to a second century in the space of four matches, driving fluently and placing his shots with precision as he found the gaps in the field remorselessly.
Bean, dropped at slip off Mir Hamza on his overnight score of 140, took advantage as he and Root took their stand to 265 at exactly a run a ball- the eighth Yorkshire highest of all time for the third wicket.
The persevering leg-spinner Mason Crane turned one sharply to bowl Bean for 173, including five sixes and 25 fours, but that only allowed Root’s England team-mate Harry Brook to join him for a stand of 72.
Root was finally trapped lbw by seamer James Harris for an imperious 156 off 165, including 21 fours, but Yorkshire still had maximum points before the new ball came.