Root has often been bracketed in the ‘Fab Four’ of Test batting, alongside Australia’s Steve Smith, Kane Williamson of New Zealand and Indian Virat Kohli.
Brook is in a new generation of run-scorers, including India opener Yashasvi Jaiswal, Sri Lankan Kamindu Mendis and New Zealand’s Rachin Ravindra.
“Brookie is by far and away the best player in the world at the minute,” said Root.
Of Root, Brook said: “I’m trying to catch him, but he’s too good, isn’t he? He’s obviously one of the best players, if not the best players, to have ever played the game. It’s mega to play with him and he’s awesome to watch.”
England sealed the series with their 323-run win in Wellington. It is their first away series win in two years and first in New Zealand since 2008.
Brook did not take the field as England completed victory on Sunday because of an ankle injury sustained playing football.
He is not thought to be a doubt for the final Test of the series in Hamilton on Saturday (22:00 GMT, Friday).
New Zealand have made a change to their squad, as opener Devon Conway misses for the birth of his first child.
Will Young is likely to take his place in the side, with Mark Chapman called into the squad.
