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The 2012 semi-finalist got off to a perfect start by breaking her Polish opponent in the opening game on No. 2 Court.
The first set was soon wrapped up 6-2 before a second set littered with breaks.
Kerber managed to hold her serve on two occasions to Radwanka's one, taking the set 6-4 to advance to the second round.
Kerber will now face Watson on Thursday after her comfortable victory earlier today.