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Problem 45: (Proving A Number Is Irrational)
Recall that we say a number $x$ is rational if there exists integers $p$ and $q\neq 0$ such that $x=p/q$. The number $\sqrt{2}$ is the positive solution to the equation $x^2=2$. Prove that $\sqrt{2}$ is not rational. [Hint: Suppose it were rational. Produce a contradiction.]
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