How long should be the smallest side of the square from which a circle of 5024 mm2 can be cut

For the square to be the smallest, the circle must be inscribed in it. Let’s draw the diagonals of the square. The point at which they intersect will be the center of the inscribed circle.
Knowing the area of a circle, we find its radius, based on the formula:
S = 3.14 * R².
R² = S / 3.14 = 5024 / 3.14 = 1600.
R = 40 mm.
The side of the square a will be equal to two radii:
a = R * 2 = 40 * 2 = 80 mm.
Answer: The smallest side of the square from which a circle of 5024 mm² can be cut is 80 mm.