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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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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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.

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?

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?

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?)