Introduction:
To find the moment of inertia of a square about an axis passing through one of its corners, we will consider the square as a system of four rods. Each rod has a mass M and a length L. The moment of inertia of an object measures its resistance to changes in rotational motion about a particular axis.

Deriving the Moment of Inertia:
To derive the moment of inertia of the square about the given axis, we can consider each rod as a point mass located at its center. This assumption allows us to use the parallel axis theorem.

Parallel Axis Theorem:
The parallel axis theorem states that the moment of inertia of an object about any axis parallel to and a distance 'd' away from an axis through its center of mass is equal to the moment of inertia of the object about the center of mass plus the product of its mass and the square of the distance 'd'.

Calculating the Moment of Inertia:
1. Consider one of the rods in the square.
2. The rod can be considered as a point mass located at its center, which is at a distance of L/2 from the corner where the axis passes through.
3. The moment of inertia of this rod about the given axis is I1 = M(L/2)^2 = ML^2/4.
4. Since there are four rods in the square, the total moment of inertia of the square about the given axis is I_total = 4I1 = 4(ML^2/4) = ML^2.

Conclusion:
The moment of inertia of the square about an axis passing through one of its corners is ML^2, where M is the mass of each rod and L is the length of each rod.