Question

how can you prove that friction is more on a rough surface as composed to a smooth surface

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Answer 1

Friction is opposing force
Rough surface has more irregularities than smooth surface.
This is the reason why rough surface has more friction than on smooth surface

Answer 2

Answer:

it is obvious. Say for example you roll a ball over two surfaces, one being smooth and the other rough, with the same force. you will notice that the ball rolls down the smooth surface easily and stops after sometime. On the other hand, while rolling the ball over the rough surface, we notice that it comes to a stop sooner than the ball rolling on the smooth surface

Explanation:

this happens because the rough surface has tiny grooves that can be visible or minute, buf they are present there. so when the ball rolls over a rough surface it comes in contact with the grooves or pits. And they, being an obstacle, would try to stop the ball. On the other hand the ball rolls smoothly on the smooth surface due to absence of grooves on it. Hence the reason.

Hope its satisfactory