Roots and Radicals

Many formulas in science, engineering, and everyday life contain roots. For example, the time an object takes to fall from a height can be modeled with a square root, while the radius of a sphere can be found from a cube root. This chapter develops the algebra needed to interpret and simplify such formulas.

Sections

• Simplify Expressions with Roots — interpreting principal roots, estimating roots, and simplifying roots of variable expressions.
• Simplify Radical Expressions — using the product and quotient properties to write radicals in simplest form.
• Simplify Rational Exponents — moving between radical notation and rational-exponent notation and applying exponent properties.
• Add, Subtract, and Multiply Radical Expressions — combining like radicals and multiplying radical expressions.
• Divide Radical Expressions — simplifying radical quotients and rationalizing denominators.
• Solve Radical Equations — isolating radicals, raising both sides to a power, and rejecting extraneous solutions.
• Use Radicals in Functions — evaluating and graphing radical functions and determining their domains and ranges.
• Use the Complex Number System — calculating with imaginary and complex numbers in standard form.

This chapter overview is adapted from Intermediate Algebra 2e, Chapter 8 Introduction by Lynn Marecek and Andrea Honeycutt Mathis, © OpenStax, licensed under CC BY-NC-SA 4.0. Access the original for free at openstax.org. Changes: condensed the introduction and recast the chapter outline as a section list.