Explain closure properties of rational numbers and irrational results from rational/irrational sums and products.
Classify a radical expression as rational or irrational after simplifying
Problem
Simplify \(\sqrt{18}/\sqrt{2}\) by combining the quotient under \(\text{one}~\text{square}~\text{root}\), then give the exact value and its classification.
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What this problem is really about
Classification should follow exact simplification, not the appearance of separate radicals. We’ll check the quotient-property conditions, combine the quotient under one square root, simplify the radicand, evaluate the principal root, and classify the resulting exact number.
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