If the circle is circumscribed on the square, meaning that the vertices of the square all lie on the circle, then the diameter of the circle is equal to the length of the diagonal of the square. Use Pythagoras on an isosceles right triangle with legs of 3 inches.
If the square is simply inside of the circle such that one or more of the square's vertices do not lie on the circle, then all you can say is that the diameter of the circle is greater than the diagonal of the square.
