Root (87) and Kevin Pietersen (53) contributed a century stand to England's cause but the tourists are staring defeat in the face again with only four wickets intact and three sessions still to play.
England struggled to 247 for six at stumps, in notional pursuit of a world-record Test victory target of 531 after Australia declared on their overnight 132 for three.
But Root hopes his side can do their country proud, and told Sky Sports: "We always want to show fight, we pride ourselves on that and obviously so far in this series we've not managed to do that so it's good to have a few guys getting some scores and showing a bit of fight.
"As a team we know we've been underperforming - that's quite evident with the scores we've got - and we're just going to have to make sure we keep fronting up and that we keep trying to challenge ourselves in practice and when we get out there make sure we get in a scrap and do our country proud."
After Australia captain Mi chael Clarke declared on their overnight 132 for three, Root says England were ready for the change and added: " We were all very prepared and we knew it was going to happen at some point this morning, so I'm sure the rest of the lads had their minds in the right place.
"Going out there we wanted to make sure we got off to a good start and get a couple of partnerships together."
The 22-year-old Yorkshire batsman has enjoyed batting at number three after Jonathan Trott left the series following the first Test in Brisbane with a stress-related illness, but says he found it hard to leave the field when he was out.
He said: " It's been great. Obviously I've only had two innings, a bad shot in the first innings - which I try not to talk about too much - but hopefully I can try and put some scores together and try to cement that spot.
"We're in a scrap, we knew that and we knew we'd have to come out fighting and that's what I was trying to do, fight for as long as I could and stay out there for as long as possible.
"I had to drag myself off. Obviously I was very disappointed. I just wanted to try to do as best a job as I could for England."
With England battling against the odds to save this s econd Test, Root is confident they can fight hard on Monday and take what they can forward and into the third Test in Perth.
He said: " At the end of the day it's Ashes cricket, it's hard cricket and that's how it should be played.
"You've just got to try and play the situation and remember that each ball is an event and reset yourself and go again.
"We're going to take whatever we can from this game and hopefully fight some more on Monday and make sure that we really front up to them and try to improve into Perth."