Week 12 — Readings & Resources
Your primary reading is Chapter 12 (in this module). Everything below is the optional, go-deeper layer — pick what helps, skip the rest.
How to use this page
This page has 10 items (4 readings and 6 videos). Allow 64–77 minutes for everything. Each group points back to the matching chapter section and class-session segment, so use the full menu when you want more practice, or take the quick path below.
Every video here has captions: turn them on with the CC button in the player. The chapter covers the same ideas in text.
Pick-one quick path (20–23 min total)
- Tutorial 5: Rational Exponents — Virtual Math Lab
- Ex: Simplify Square Roots - Not Perfect Roots — Mathispower4u
- Checking For Extraneous Solutions of Radical Equations — The Organic Chemistry Tutor
① How do I tidy up a square root? Roots and the product rule
Chapter 12, Section “Simplify a square root with the product rule” · Session 1, Segment 2, “Simplifying square roots” · Remember: pull out the largest perfect-square factor, and never split a root over a sum.
- Radicals: Introduction & Simplification — Purplemath — a step-by-step page that treats a root as the undo of a power and then pulls perfect-square factors out from under the root sign, with several numeric examples to check yourself against; use it while working through the Week-12 module overview. (reading, 8–12 min)
- Ex: Simplify Square Roots - Not Perfect Roots — Mathispower4u — short worked examples of finding the largest perfect-square factor and writing the answer as a whole number times a root. (video, 4 min) (captions: creator)
- How To Simplify Radicals — The Organic Chemistry Tutor — many radicals simplified in a row, including square roots with letters under the sign; pause after each one and try it first. (video, 13 min) (captions: automatic)
② What does a fraction in the exponent mean? Rational exponents
Chapter 12, Section “Read a rational exponent as a root” · Session 2, Segment 5, “Rational exponents” · Remember: the bottom number of the exponent is the root, the top number is the power, and you take the root first.
- Tutorial 5: Rational Exponents — Virtual Math Lab — a short tutorial that reads the bottom of a fraction exponent as the root and the top as the power, advises taking the root first so the numbers stay small, and then simplifies with the usual exponent rules. This builds on Week 1's work with the exponent rules. (reading, 6–9 min)
- Evaluating Numbers with Rational Exponents by using Radical Notation - Basic Example 1 — Patrick J — one careful example of rewriting a fraction exponent as a root and evaluating it without a calculator. (video, 6 min) (captions: automatic)
- Ex: Simplify Expressions with Rational Exponents — Mathispower4u — the exponent rules applied to fraction exponents, with the common-denominator step shown each time. Stop here before exponential functions; next week takes that up. (video, 3 min) (captions: creator)
③ Why must I check every answer? Radical equations
Chapter 12, Section “Check every candidate: extraneous solutions” · Session 2, Segment 8, “Extraneous solutions” · Remember: isolate the radical, square both sides, and put every candidate back into the original equation.
- Solving Radical Equations - Steps & Examples — ChiliMath — a worked set that runs from easy to harder equations, isolating the radical before squaring and checking each answer for an extraneous solution. (reading, 8–12 min)
- Checking For Extraneous Solutions of Radical Equations — The Organic Chemistry Tutor — several equations where squaring produces a candidate that fails, and how substitution catches it. (video, 10 min) (captions: automatic)
- Solving a Radical Equation When You Have One Extraneous Solution — Brian McLogan — a short single equation that squares into a quadratic, factors, and keeps only the candidate that checks. (video, 3 min) (captions: automatic)
Optional one-stop reference (free online reference)
- nth Root — Wolfram MathWorld — a mathematics encyclopedia's entry; read the opening definition, the root-sign and fraction-exponent notations, and the principal root, and skip the later material on complex roots, which goes beyond this course. (reading, 3–5 min)
Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell your instructor and use the reference above in the meantime.
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