Explain closure properties of rational numbers and irrational results from rational/irrational sums and products.
Classify a sum of a rational number and an irrational number
Problem
Classify \(3+\sqrt{2}\) as rational or irrational and justify the classification using the rule for adding a rational number to an irrational number.
Big Picture
What this problem is really about
Adding a rational number cannot turn an irrational number rational. We’ll classify each addend, suppose the sum were rational, subtract the rational addend using closure, and expose the contradiction that the known irrational term would then have to be rational.
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