Circular motion help

Hello,

I have a question I just cannot get to the bottom of. Can someone please point out what I'm doing incorrectly before I go insane?

Question:
A particle travels at a constant speed around a circle of radius r with centripetal acceleration a. What is the time taken for ten complete rotations.

The answer is 20π ×√(r/a)

I tried using the a=w²r equation initially. Replacing w=2π/T

-This gave me a=(2π/10T)²r

-Then I did √(a/r) ×1/2π=10T

-And then √(r/a) ×2π=10T

And I couldn't go any further.
I think I'm either using the 10 rotations incorrectly or I rearranged incorrectly.