Week 12 · Module overview

Week 12 — Radicals, Rational Exponents & Radical Equations

College Algebra Free sample edition

Welcome to your Week 12 Start Here page.

Why this matters

Roots turn an area back into a length for a landscaper and a drop height into a fall time for a safety engineer. Check every answer, because squaring can hand you one that never worked.

In plain language

This week you learn to run a power backwards. If you know a garden's area, a root (the number that, multiplied by itself the right number of times, gives back what you started with) tells you the length of its side. You will learn to tidy up a root so it is easy to read, and to write a root as a fraction in an exponent, called a rational exponent (an exponent that is a fraction, such as two thirds). Then you will solve equations with the unknown hidden under a root. Squaring both sides of such an equation can hand you an answer that never worked, so you will check every answer you find.

Already covered: Week 1 set the exponent rules; Week 3 named the radicand; Week 6 built the special products; Week 7 solved quadratics; Week 11 met extraneous solutions.
This week: roots and radicals, the product and quotient rules, rational exponents, and radical equations with their checks.
How they connect: a rational exponent obeys the exact Week 1 rules, and solving a radical equation often ends in a Week 7 quadratic.
Where we're going next: Week 13, Exponential Functions, moves the variable up into the exponent itself, so your exponent rules carry straight into the next unit.

Focus

How do you run a power backwards, and how do you know an answer you found really works?

By the end of this module, you should be able to:

[ ] simplify a square root with the product and quotient rules
[ ] read a fraction exponent as a root, root first
[ ] simplify with the exponent rules on fraction exponents
[ ] solve a radical equation and reject an extraneous solution

To-do

Plan your week

Read Chapter 12 (about 45 minutes), then the lecture and slides.
Work the lecture tutorial (60–90 minutes) and the practice set (about 20 minutes).
Do the Model/Build Studio (about 90 minutes), the discussion, and the assignment.
Take the quiz.

This week's checkpoint: simplify √48 and solve √(x + 3) = x + 1, checking both candidates.

You've got this

Go in order, and ask your instructor early if a step snags.

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