The 24-year-old Yorkshireman, regarded as a captain in waiting, has scored England's only two hundreds of the ongoing Ashes series to help put his side an unbeatable 3-1 up against Australia heading into Thursday's fifth and final Test at The Oval.
Such has been Root's form during the past two months, he has displaced Australia's Steven Smith at the top of the International Cricket Council's Test batting rankings, with England paceman Stuart Broad now his main rival for man-of-the-series honours in the Ashes.
"I've never seen a player improve like that."
Cook said Root's style was similar to that of New Zealand rising star Kane Williamson, who has also played for Yorkshire and was lauded earlier this season by the county's former England opening batsman Geoffrey Boycott as someone good enough to have played on uncovered pitches.
"It reminds me a little bit of Kane Williamson. Those two are very classical players . . . You watch them play a Twenty20 knock or (in) a Test match and they're still doing very similar things.
Meanwhile, Cook said a more positive approach had helped his side neutralise the impact of Australia fast bowler Mitchell Johnson, although he accepted local conditions had played their part as well.
Left-arm quick Johnson took a remarkable 37 wickets at under 14 apiece during Australia's 5-0 home whitewash of England in the 2013/14 Ashes.
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