Math CentralQuandaries & Queries


Question from prateet, a student:

prove that root2 is an irrational number.

I'll start you with a hint. Because "irrational" is a negative concept, a proof by contradiction is a good bet.

Suppose root(2) was rational. What does that mean: That it would be p/q.

We can assume "for free" that it's in lowest terms, so we do.

What else can you deduce from this based on the asumption that this is root(2)?

Now look for a contradiction. Hint: are p and q odd or even?

Good Hunting!

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