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Chapter 27.1
Solving radical equations
What You'll Learn
Isolate the radical expression on one side of the equation
Square both sides to eliminate square roots and solve algebraically
Identify and reject extraneous roots by substituting answers back into the original equation
Apply algebraic expansion formulas when squaring binomials with radicals
Recognize when squaring both sides can introduce invalid solutions
What You'll Practice
1
Solving equations with one radical by isolating and squaring
2
Solving equations with two radicals by separating them before squaring
3
Factoring quadratic equations that result from squaring radical expressions
4
Verifying solutions by substitution to eliminate extraneous roots
Why This Matters
Mastering radical equations is essential for higher algebra, precalculus, and physics. You'll use these techniques to solve distance formulas, work with quadratic relationships, and handle complex equations in calculus. Understanding extraneous roots teaches you to verify solutions critically.
Before You Start — Make Sure You Can:
This Unit Includes
8 Video lessons
Practice exercises
Skills
Radical Equations
Square Roots
Extraneous Roots
Quadratic Equations
Factoring
Algebraic Verification
Isolating Variables
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