Final answer:
To find the difference in the side length of two cubes with different surface areas, use the formula for the surface area of a cube and solve for the side length. The difference is 2 inches.
Step-by-step explanation:
To find the difference in the side length of two cubes with different surface areas, we first need to find the side length of each cube. We can use the formula for the surface area of a cube, which is given by 6s^2, where s is the side length.
For the cube with a surface area of 1,200 square inches, we can rearrange the formula to solve for s, which gives us s = sqrt(1200/6) = 10 inches.
For the cube with a surface area of 768 square inches, we can rearrange the formula to solve for s, which gives us s = sqrt(768/6) = 8 inches.
Therefore, the side length of the larger cube is 10 inches and the side length of the smaller cube is 8 inches. The difference in side lengths is 10 - 8 = 2 inches.