Learning Goal
Part of: Use properties of rational and irrational numbers — 1 of 1 cluster items
Explain operations on rational and irrational numbers
**HSN.RN.B.3**: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
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HSN.RN.B.3: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
What you'll learn
- Explain why the sum or product of two rational numbers is always rational, using a general algebraic argument (not just examples)
- Explain why the sum of a rational number and an irrational number is always irrational, using proof by contradiction
- Explain why the product of a nonzero rational number and an irrational number is always irrational, using proof by contradiction
- Identify the key role of the "nonzero" condition: explain why 0 times an irrational number is rational, and why the general product rule requires the rational factor to be nonzero
- Classify expressions like 3 + √2, (1/2) · √5, or 7 + √9 as rational or irrational and justify the classification using the learned arguments
Slides
Interactive presentations perfect for visual learners • Interactive presentation
Slide Video
Watch narrated slides play like a video lesson • Narrated slide playback
Task-sets
Learning resource • 1 task-sets