6-5 Solving Square Root and Other Radical Equations
Objective
To solve square root and other radical equations
Lesson Vocabulary
- radical equation
- square root equation
A radical equation is an equation that has a variable in a radicand or a variable with a rational exponent. If the radical has index 2, the equation is a square root equation. In this lesson, assume that all radicals and expressions with rational exponents represent real numbers.
Essential Understanding Solving a square root equation may require that you square each side of the equation. This can introduce extraneous solutions.
To solve a radical equation, isolate the radical on one side of the equation. Then raise each side to the power suggested by the index.
Problem 1 Solving a Square Root Equation
What is the solution of
Think
Do you need to introduce
No, when you take the square root of each side of an equation you do, but here you are squaring both sides of the equation.
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions