# Homework Help: Proving pi is irrational

1. Dec 14, 2012

### 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

2. Dec 14, 2012

### 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.

3. Dec 14, 2012

### phospho

that makes much more sense, heh.