Week 12 — Readings & Resources · Radicals, Rational Exponents & Radical Equations

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective covered: Objective 7 — Simplify radical expressions; convert between radical and rational-exponent form; simplify expressions with rational exponents; solve radical equations, checking for extraneous solutions.

How to use this page

Everything here is a link to an external resource — open it in your browser, the same way you'd open a YouTube link. Nothing needs to be downloaded.

This week's load is ~3 readings + ~2 videos, grouped by the four lecture ideas. Read or watch one item per group and you're ready for the quiz; do all of them and you'll be very comfortable. Total time is roughly 35–50 minutes if you do everything, far less if you pick one per group.

Reading order that matches the lecture: ① simplify radicals (product/quotient rules + the sum misconception) → ② rational exponents (definition + conversions) → ③ simplifying expressions with rational exponents → ④ solving radical equations (isolate → raise to power → solve → check).

This week's critical habit: every reading this week eventually gets to the check step for radical equations. Don't skip it in the readings any more than you'd skip it on the quiz.

① Simplifying Radicals

Maps to Lecture Segments 2–3. The product rule splits a product; it never splits a sum. Factor out the largest perfect-square before pulling anything out.

Reading — "Radicals and Rational Exponents" (OpenStax, College Algebra 2e, §1.3)
🔗 https://openstax.org/books/college-algebra-2e/pages/1-3-radicals-and-rational-exponents
Why it's assigned: covers the product and quotient rules for radicals, simplifying expressions with and without variables under the sign, and the definition of rational exponents — the full scope of the week's first three topics in one section. Worked examples match the class approach.
⏱ ~12 min

Reading — "Radicals" (Paul's Online Math Notes — Algebra)
🔗 https://tutorial.math.lamar.edu/classes/alg/Radicals.aspx
Why it's assigned: a tightly written, example-dense page that nails simplification technique — including the critical misconception that √(a+b) ≠ √a+√b — and explains when and why the product rule works. A strong second pass or substitute if you prefer Paul's style.
⏱ ~9 min

② Rational Exponents

Maps to Lecture Segment 4. The denominator of the exponent is the root; the numerator is the power. Always take the root first on a whole number.

Reading — "Rational Exponents" (Paul's Online Math Notes — Algebra)
🔗 https://tutorial.math.lamar.edu/classes/alg/RationalExponents.aspx
Why it's assigned: clear, example-rich treatment of a^(m/n) = (ⁿ√a)^m, including the conversion rules (radical ↔ rational exponent) and evaluating expressions like 8^(2/3) and 16^(3/4). Builds directly on the radicals page above.
⏱ ~8 min

(The OpenStax §1.3 link above also covers rational exponents in the same section — use whichever treatment clicks better.)

③ Simplifying Expressions with Rational Exponents

Maps to Lecture Segment 5. Same-base rules from Week 1 apply; fraction arithmetic for the exponents.

Both the OpenStax §1.3 page (① above) and the Paul's Rational Exponents page (② above) include worked examples of simplifying products, quotients, and powers of rational-exponent expressions. After reading either of those, the simplification rules in this segment are a natural extension — no additional reading is needed.

④ Solving Radical Equations

Maps to Lecture Segments 6–7. Isolate → raise to the power → solve → always check. The check is non-optional.

Reading — "Equations with Radicals" (Paul's Online Math Notes — Algebra)
🔗 https://tutorial.math.lamar.edu/classes/alg/SolveRadicalEqns.aspx
Why it's assigned: the tightest treatment of the four-step method — with detailed extraneous-solution examples showing exactly where the spurious root appears and how the check catches it. Ideal as a step-by-step reference before attempting the assignment.
⏱ ~10 min

Reading — "Solve Radical Equations" (OpenStax, College Algebra 2e, §2.6 — radical equations portion)
🔗 https://openstax.org/books/college-algebra-2e/pages/2-6-other-types-of-equations
Why it's assigned: OpenStax §2.6 covers radical equations in the context of "other types of equations." The radical-equations section includes worked examples with extraneous solutions and the important real-world connection (the pendulum formula uses a square root). Scroll to the "Solving Radical Equations" heading.
⏱ ~10 min

Video — "Intermediate Algebra Lecture 10.2: Rational Exponents; From Radicals to Rational Exponents" (Professor Leonard)
🔗 https://www.youtube.com/watch?v=p56S2R1a1GM
Why it earns the click: a detailed, whiteboard-paced walkthrough of converting between radical and rational-exponent form and evaluating rational-exponent expressions — exactly the Week-12 conversion skill. Professor Leonard works every step out loud, making it ideal if you want to see someone do it slowly.
⏱ longer lecture (skim to the parts you need; first 30 minutes cover conversion and evaluation)

Optional one-stop reference (free online)

If you'd like one optional reference to return to through the end of term:
🔗 Paul's Algebra notes (index): https://tutorial.math.lamar.edu/classes/alg/alg.aspx
🔗 Professor Leonard — College Algebra / Trigonometry playlist: https://m.youtube.com/playlist?list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP
Why they're here: reputable, currently-available references that cover every remaining topic in Weeks 13–16 (exponential and logarithmic functions and equations) — entirely optional, useful for reference or extra practice.

Pick-one quick path (≈20 min total)

In a hurry? Do exactly these and you'll be ready for the quiz:
1. Read OpenStax §1.3 — Radicals and Rational Exponents (covers groups ① and ②).
2. Read Paul's — Equations with Radicals (group ④, including the extraneous-solution examples).

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell Prof. Calloway and use the Paul's Online Math Notes index above in the meantime.