A10-kilogram box is at static equilibrium, and the downward pull of gravity acting on the box is 98 newtons. what is the minimum force that would be required to just pick up the box?

The box is at equilibrium, so the net force on the box is zero (the force of gravity on the box is equal to the force exerted up on the box by the surface on which it rests.)
To pick up the box, our upward force must be greater than the force of gravity on the box (the weight). So, we must lift up the box with a force greater than 98 newtons. :)