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Circling The Square Puzzle

The Puzzle:

In the diagram below, each circle is just big enough to touch all four sides of the square. The area of the square is therefore just a bit more than the area of one of the circles.

I want to know how many of the circles you need to cover the whole square. Is 2 enough? Or do you need 3? Or 4? Or more?

I have put 5 circles for you to play with (print and then cut them out), but what is the least number you need?

Do you have the answer? Check against our solution!