Prove that if $n>1$ then between $ n $ and $n^2$ is at least one prime.

Question

Prove that if postive intetger $n>1$ then between $ n $ and $n^2$ is at least one prime.

I have known this stronger reslut:https://en.wikipedia.org/wiki/Bertrand%27s_postulate

But my problem is constant math test,so I guess maybe there exist more simple methods? and I want to have prove $$\pi(n^2)-\pi(n)>1,\forall n>1$$