Interview Question: Irrational Proof

Sample Question #281 (mathematical breainteaser)

Can you prove that sqrt(2) [the square root of 2] is an irrational number?

[Taken from Chapter 2 of Zhou, A Practical Guide to Quantitative Finance Interviews]

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4 Responses to Interview Question: Irrational Proof

  1. Brett says:

    ANSWER
     
    I’ll just give you a hint (to tease you, of course!): prove by contradiction!
     
    BTW, if you don’t know what an irrational number is, time to reconsider your career goals! (I’m serious.)
     
    For detailed solution, see p.31 of A Practical Guide to Quantitative Finance Interviews.

  2. quantyst says:

    To do justice to the question, it should be called "Irrational" proof.  I mean: do you really mean the proof is irrational?  If so, then why would it be called a proof in the first place?A more appropriate name would be "Irrationality Proof".  Do you agree?

  3. quantyst says:

    CORRECTION!To do justice to the question, it should NOT be called "Irrational" proof. 
    I mean: do you really mean the proof is irrational?  If so, then why
    would it be called a proof in the first place?A more appropriate name would be "Irrationality Proof".  Do you agree?

  4. Brett says:

    quantyst, the question title was meant to be a joke… or, rather, a pun. 🙂  Some interviewers do have a sense of humor!  (But seriously, during real-life interviews no interviewer will announce a question with a title. Only books and blogs use titles, right?)

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