Cook played the third longest innings of Test cricket in scoring 263, batting for four minutes short of 14 hours on the fourth day of the first Test against Pakistan in Abu Dhabi on Friday.
That lifted England to 569-8, 46 ahead of Pakistan’s first innings score of 523-8 declared.
Root said Cook’s knock typifies his concentration and will.
“It was a hell of an effort,” said Root of Cook’s innings behind Pakistan’s Hanif Mohmmad (970 minutes) and South African Gary Kirsten (878 minutes).
“Two days in that heat showed huge amounts of skill, concentration and fitness. We spoke a lot about batting long periods of time out here and how important it will be if we are to give ourselves a chance of winning.
“Our captain has led from the front and set the example for the rest of the series. It gives us a glimmer of hope tomorrow that we can get some sort of result.”
Cook added 141 for the fourth wicket with Root, who made an attractive 85, and another 91 for the sixth with Ben Stokes, who scored 57.
Cook was finally out, caught sweeping off spinner Shoaib Malik at deep square-leg, a dismissal Root said would have left the England captain disappointed after missing an elusive triple hundred.
“I’m sure he would have, I haven’t had the chance to speak to him, the fact is he’s out and we are in a position…that we have a chance to win this game. We can put Pakistan under pressure and hopefully force the result,” said Root.
Root praised Pakistan’s bowling, led by paceman Wahab Riaz, who took 3-116.
“I think they’ve all bowled exceptionally well, at no point did we feel we could take the game away from them even when we’ve built big partnerships. They have controlled the economy rates very well and it was hard to score freely,” said Root.
Root believed England’s fight puts them in good stead for the three-match series with the second Test in Dubai (October 22-26) and third in Sharjah (November 1-5).
“There has been a lot of talk about our preparation,” said Root of the training after winning the Ashes back home in August.
“It’s not been a massive amount but the quality of it was right up there and it set us up nicely. We spoke before about what we wanted to do and have done it throughout this game.”