It was former England captain and current batting coach Gooch, as Cook's mentor at Essex, who famously nurtured the talent which has taken his protege to the top tier of international cricket.
Cook has gone on to surpass even Gooch himself, among others, as England's most prolific Test centurion of all time.
After Root's man-of-the-match 180 as England trounced Australia by 347 at Lord's, to go 2-0 up with three to play in this summer's Investec Ashes series, Gooch was happy to substantiate comparisons between the 22-year-old Yorkshireman and his Test captain.
"They are both mature for young men, and Alastair Cook had a similar mentality when he was Joe's age," said Gooch, struck by Root's potential from the moment he first had a good look at him on tour in India last winter.
"He was mature in the mind - he knew exactly how he could score runs - and I think anyone who saw Joe saw that too.
"When he was suddenly promoted to the one-day side, he walked straight in, and you'd have thought he'd been playing this sort of game the whole time."
Root added Twenty20 and one-day international debuts to his maiden Test, in Nagpur, in a matter of weeks - and has rarely looked back since, most recently making a success of his move up the order to open alongside Cook.
It is as much the 22-year-old's attitude of mind as his batting ability which impresses record first-class runscorer Gooch.
"Every player wants to improve themselves, but generally in a coach-player relationship the player's the master.
"You offer observations as a coach and ideas and advice, but if it's a two-way thing ... the player is keen to receive information and is actually seeking knowledge ... you're more likely to make some progress
"Joe, from the first time we saw him in India, was an impressive young character.
"I'm not surprised at all that he's moving forward with his skill levels, the way he works at his game and all the disciplines that are in place."
Root's breakthrough century at Lord's - his second for England in Tests but his first at the top of the order - has inevitably raised expectations again.
"Every individual handles it differently," said Gooch.
"It's early days. But I have nothing to suggest to me that Joe won't continue to be a successful player at international cricket.
"A lot of things can come along and test you, so we'll wait and see.
"The jury's out on that, but at moment he's going in the right direction."
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