R.3 Rational Exponents and Radicals

Miller & Gerken, College Algebra 2e — Pages 32-43

Learning Objectives

  • Simplify expressions containing radicals

  • Convert between radical notation and rational exponents

  • Apply properties of radicals

  • Add, subtract, multiply, and divide radical expressions

Key Concepts

Radical to Exponent Conversion

\[\sqrt[n]{a} = a^{1/n}\]
\[\sqrt[n]{a^m} = a^{m/n}\]

Properties of Radicals

\[\sqrt[n]{ab} = \sqrt[n]{a} \cdot \sqrt[n]{b}\]
\[\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}\]
\[\sqrt[m]{\sqrt[n]{a}} = \sqrt[mn]{a}\]

Examples

Example 1. Example 1 (p. XX)

Work through textbook example…​

Practice Problems

Problem 1 (p. XX, #YY)

Problem:

My Work:

Answer:

Section Summary

  1. Key point 1

  2. Key point 2

  3. Key point 3

Study Notes

Personal observations and things to remember…​

Next: R.4 Polynomials