How to prove: $2^\frac{3}{2}<\pi$ without writing the explicit values of $\sqrt{2}$ and $\pi$ How to prove: $2^\frac{3}{2}<\pi$  without writing the explicit values of $\sqrt{2}$ and $\pi$.
I am trying by calculus but don't know how to use here in this problem. Any idea?

Say $\sin x\leq x$ with $x=\dfrac{\pi}{6}$ we get $\dfrac12\leq\dfrac{\pi}{6}$ or $3\leq\pi$ and $8<9\leq\pi^2$.
