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It was a fairly even contest at the start of the opening set, with both players searching for that vital break of serve, but it came to the Polish pro, who held instantly.
After grabbing another break point, Radwanska went on to take a one-set lead in Melbourne, while Muguruza came away from the first set with 20 unforced errors.
The second set was more even between the pair, with Muguruza managing to hold her serve, but once again, Radwanska got the first break point to push on and wrap up the clash.
Radwanska will take on Victoria Azarenka in the quarter-finals.