Discrete Math Quiz
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PROBLEM-SOLVING & DISCRETE MODELING
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A student claims to prove that "2\sqrt{2} is irrational" using the following approach: "Assume 2=pq\sqrt{2} = \frac{p}{q} where pp and qq are integers with gcd⁡(p,q)=1\gcd(p,q) = 1. Then 2q2=p22q^2 = p^2, so p2p^2 is even, which means pp is even. Let p=2kp = 2k, then 2q2=4k22q^2 = 4k^2, so q2=2k2q^2 = 2k^2." What is the most critical error in the student's reasoning at this point?
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