Back to Explain operations on rational and irrational numbers — Problem 5 · Task Set 3
Exercises: Explain Why Sums and Products of Rational and Irrational Numbers Follow Specific Rules
Work through each section in order. For explanation problems, write in complete sentences and include the reasoning (proof template, counterexample, or construction). Classification alone is not sufficient — explain why.
Grade 9·21 problems·~32 min·Common Core Math - HS Number and Quantity·standard·hsn-rn-b-3
Work through problems with immediate feedback
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Fluency Practice
For each problem, classify the expression and provide the required argument or proof.
1.
Prove by contradiction that is irrational. Then explain specifically why the proof requires the factor 3 to be nonzero — what goes wrong if we try to apply the same argument to ?