Is the Square Root of Pi Irrational?

[phospho]

A question in my book says to prove that pi is irrational, I found a proof which I'm happy with and found a similar one on the web however on the solutions they have done:

assume √π is rational i.e $$\sqrt{\pi} = \frac{p}{q} p,q \in \mathbb{Z}$$
$$\pi = \frac{p^2}{q^2}, p^2,q^2 \in \mathbb{Z} ∴ \pi \mathrm{is\ rational}$$

∴ contradiction √π irrational,

could anyone explain how it's a contradiction? I've pasted exactly what they have in the solution

 

[haruspex]

The proof shows that if pi is irrational then so is its square root. Presumably that is what the question asked, or intended to ask.

 

[phospho]

The proof shows that if pi is irrational then so is its square root. Presumably that is what the question asked, or intended to ask.

that makes much more sense, heh.