At the end of a dominating second session, England had reached 351-3, trailing by 205 runs, with Root (119) and Brook (64) on the crease.
Pakistan got rid of dangerous Ben Duckett early in the second session with Aamir Jamal providing the breakthrough. The left-hander played a quick-fire knock of 84 runs from 71 balls, laced with eleven boundaries.
Brook joined Root and together they added an unbeaten 110 runs in 133 balls for the fourth wicket until the umpires called the Tea on Day 3.
England scored 232-2 at Lunch on Day 3 with Ben Duckett and Joe Root on the crease with scores of 80 and 72 respectively.
Pakistan got the early breakthrough in the morning as they removed set England batter Zak Crawley, who was playing at 78 runs from 85 balls.
However, following the dismissal, Duckett joined Root, and together, they attacked Pakistan bowlers, constructing a 119-run stand for the third wicket in 124 balls.
Duckett, who could not open the innings yesterday due to a finger injury, particularly played aggressively with a strike-rate of over 100. Meanwhile, the in-form Root continued to show his elegant strokeplay.
At the Stumps on Day 2, England were 96/1 with Crawley, unbeaten with a run-a-ball, 64 and Joe Root, 32 not out, at the crease.
The touring side had a shaky start to their first innings as they lost their interim captain Ollie Pope for a two-ball duck.
But Crawley made an astounding recovery for England with a brisk knock while Root played cautiously until the end of the play.
Aamir Jamal
Returning Aamir Jamal claimed the solitary wicket for Pakistan on the second day.
Prior to that, Pakistan lost two wickets in quick succession in the third session after putting up a mammoth 556-run total.
Abrar Ahmed (3) was the last wicket to fall, falling prey to part-time bowler Joe Root. Prior to that, Shaheen Shah Afridi, who scored a crucial 26 runs, was bowled by Jack Leach.