Murray setting his mind towards tougher tests ahead
Murray cruised past Jurgen Melzer, winning 6-3 6-1 6-1 in an hour and 44 minutes to maintain his record of having not dropped a set in the tournament.
The British No 1 produced a mature, controlled performance, contrasting sharply with that offered by Melzer, the Austrian spraying the ball all over Rod Laver Arena as his all-or-nothing game was woefully exposed.
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Hide AdMurray will meet Alexandr Dolgopolov in the last eight after the Ukrainian stunned fourth seed Robin Soderling in a five-set thriller.
With Rafael Nadal and Roger Federer potential opponents in the semi-final and final, Murray accepts straight-set wins may be a thing of the past.
He said: "I feel good but the matches are definitely going to get tougher.
"I'm not expecting to go through the tournament winning matches like that, with that scoreline. So I'm ready for that mentally when it does get tough."
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Hide AdMurray again got off to a good start, as he has done in the majority of his matches in Melbourne.
"I started very well, hitting the ball very cleanly right from the beginning of the match," he added.
"There was a few games where it was tough from one of the ends. It doesn't feel it when you're watching, but all the players will tell you from the far side of the court, it is difficult.
"I came through a couple of tough service games from that side. But when I had the wind with me, I dictated a lot of the points, returned very well, served well in the second and third sets."
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Hide AdNadal fired out a warning by beating Marin Cilic and then declaring himself back to full fitness.
The Spaniard, who is bidding to become the first man since Rod Laver in 1969 to hold all four grand slams simultaneously, set up a quarter-final against countryman David Ferrer after seeing off the big-serving Croatian 6-2 6-4 6-3.
Ferrer ended the run of Canadian qualifier Milos Raonic, winning 4-6 6-2 6-3 6-4.
Kim Clijsters reached the women's quarter-finals although she was made to struggle by Ekaterina Makarova before finally edging through 7-6 (7/3) 6-2.
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Hide AdClijsters meets Agnieszka Radwanska, who had a 7-5 3-6 7-5 victory over Shuai Peng.
Vera Zvonareva is on course for a third successive grand slam final appearance after a 6-4 6-1 victory over Iveta Benesovaset. She faces Petra Kvitova, who had a three-set win over Flavia Pennetta.