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Proving pi is irrational

  1. Dec 14, 2012 #1
    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 [tex] \sqrt{\pi} = \frac{p}{q} p,q \in \mathbb{Z} [/tex]
    [tex] \pi = \frac{p^2}{q^2}, p^2,q^2 \in \mathbb{Z} ∴ \pi \mathrm{is\ rational} [/tex]

    ∴ contradiction √π irrational,

    could anyone explain how it's a contradiction? I've pasted exactly what they have in the solution
     
  2. jcsd
  3. Dec 14, 2012 #2

    haruspex

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    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.
     
  4. Dec 14, 2012 #3
    that makes much more sense, heh.
     
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