He may not be a great captain yet but Silverwood said he will get there eventually.
"Seeing him become England's most successful captain was superb. It's something I've been looking forward to for a while. He's in a great place at the moment and I'm really enjoying watching him.
"I think he's a good Test captain. He is growing and learning all the time. We saw that last week. There's potential there for him to be one of the great England captains. If we win in Australia, we can have this conversation again."
Root had made some tactical errors at Lord's which cost the team the match.
"He reflected on the Lord's Test and some of the decisions he made. He does learn as he goes along and that's a great characteristic for a captain to have: to reflect back honestly and make a difference. And he's certainly made a difference this game," said Silverwood.
The coach said there is a possibility that in-form pacers James Anderson and Ollie Robinson could be rested for the foruth Test, starting September 2, as part of workload management with both having played three on the trot.
"What I don't want to do is break them," Silverwood said referring to Anderson and Robinson.
"We've got a lot of cricket in front of us. The Tests are coming thick and fast now. They're back-to-back. It is difficult. These guys are giving everything, every day when we're out on the field.
"We've got to make sure we're looking after them, but I won't be making any decisions or judgments right now until we get to London."