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'He was one of the great teammates,' said Cook on BBC’s Test Match Special.
Root went the 10,000-run mark in the first Test against New Zealand to become just the 14th cricketer to score 10,000 Test runs.
What set Cook apart from his contemporaries was his insatiable appetite for runs, which made him the highest run scoring left-handed batsman in Test cricket.
Cook has endured a poor run of form with the bat in nine tests this year in which he has averaged 18.62 runs compared with a career average of 44.88.
With 406 runs required on the final day and seven wickets in hand, an embarrassing 1-4 series defeat looks imminent for India as of now.
The final match at the Oval is only of academic importance but Virat Kohli will want to finish on a definite high.
Cook said it would have been very embarrassing for him if Pujara had stopped the overthrow and he had started celebrating since he had not noticed the latter chasing the ball.
Cook, who will play his 161st test starting on Friday, retires as the sixth highest scorer in test cricket.
Eoin Morgan's top-ranked men enter the tournament as the one of the most consistent teams in the format and their quest for a first 50-overs title begins against South Africa at the Oval on May 30.
Results 1-9
