Study Guide — HSN.RN.B.3
Explain why the sum or product of two rational numbers is rational; t…
Extend understanding of real numbers — radicals, exponents, and rational exponents.
What this standard means
- 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.
- Apply explain why the sum or product of two rational numbers is rational; t… with models and explanation
- Simplifies radical expressions
_See printable PDF for diagram._
How to use the 20 practice sets
| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |
Pacing: 10–15 minutes per session.
How to practice
1. Simplify radicals by factoring perfect squares 2. Apply exponent rules step by step 3. Rationalize denominators when needed
_See printable PDF for diagram._
Common mistakes
- Adding radicals with different radicands
- Exponent rule misuse
Review and practice tests
1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for HSN.RN.B.3.
- [ ] Simplifies radical expressions
- [ ] Applies rational exponent rules
- [ ] Explains steps using properties
Materials for this standard
- Practice Problems — 20 printable sets
- Review — 10 difficulty levels
- Practice Test — 10 difficulty levels
- Answer key — for parents and tutors