Cook, who marked his 50th Test as England captain by winning the toss, was 40 not out and Root unbeaten on 41, with the hosts looking to bounce back from losing last week's first Test at Lord's.
England's second-wicket partnership was so far worth 70 runs after Hales was bowled by a superb Mohammad Amir delivery for 10.
Predictably, there were a few jeers as Amir prepared to bowl the first ball of the match.
Amir, who took the last wicket in Pakistan's win in the first of this four-Test series, saw his first and second deliveries edged through gully for four by Cook.
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Cook also seized on a short and wide Rahat Ali delivery which he cut for four.
Amir, one of three left-arm quicks in Pakistan's attack with Rahat and Wahab Riaz, had Hales dropped in the gully on six by Asad Shafiq, the ball speeding away to third man for four.
The delivery also cut off the seam a touch and knocked over Hales's middle and off stumps.
England were now 25 for one after seven overs.
Root got off the mark with a straight driven four off Rahat.
Leg-spinner Yasir Shah, England's tormentor-in-chief at Lord's with 10 wickets, saw his second ball Friday cut in front of point by Root for four.
That shot brought up England's fifty in 92 balls with 10 boundaries.
Left-hander Cook then cashed in on a rare Shah short ball with a pull to the mid-wicket rope.