Homework 8th grader: $\pi^2$ is irrational

Maybe the author made a mistake, and meant to ask something like "is $\sqrt{\pi}$ irrational?"? Or maybe the author just intends to spark open-ended curiosity.

If there was an elementary standalone proof that $\pi^2$ was irrational, then it would imply $\pi$ was too. But I don't think there is a straightforward proof for $\pi$.

Making use of the given that $\pi$ is irrational doesn't help either of course.

Hermite's proof that $\pi^2$ is irrational is here (found via a Google search for proof that pi squared is irrational ): http://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational

The identity: $$ \pi^2 = 18\sum_{n\geq 1}\frac{1}{n^2\binom{2n}{n}} \tag{1}$$ comes from the Euler series acceleration method and it can be used to prove the irrationality of $\pi^2$ and even more, for instance providing a (rather crude) upper bound for the irrationality measure of $\pi^2$. In fact, the existence of an identity similar to $(1)$ is the key of Apery's proof about the irrationality of $\zeta(3)$. However, I wouldn't try to prove $(1)$ or to explain a good portion of the technicalities of diophantine approximation to an $8$th-grader, no matter how brilliant he/she is.