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A concussed Smith was ruled out of the third test, starting at Headingley on Thursday, after being struck in the neck by a vicious bouncer from England paceman Jofra Archer.
Root said the loss of Smith, who has scored 144, 142 and 92 in three innings so far, was similar to England missing paceman James Anderson who is unavailable after suffering a calf injury in the first test.
"We had the challenge of Jimmy going down four overs into a test and had to manage without a replacement, so you get these swings within a big series... when you get your opportunity you've got to jump on it," Root told reporters.
"When you play against someone of (Smith's) quality, you're trying to find a number of different ways to get him out. The way that Jofra bowled in that spell... we felt like we were creating chances all the time.
"But you never want to see someone go off injured. There was a lot of concern in our dressing room for his health and it's great to see that he's up and about."
England added Ollie Pope to their squad as a standby after fellow batsman Jason Roy was struck on the neck during training on Tuesday.
"Jason has been monitored quite closely, as you'd expect. He's undergone a couple of concussion tests so far and scored really well, so as it stands I fully expect him to be fit and ready to play tomorrow," Root said.
Australia lead the five-match series 1-0 after winning the first test by 251 runs. The second test was drawn.
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