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Advanced Mathematics 2200
Algebra and Number
16. NL.SO.2200AN3
16.1 Solving radical equations
Solving Radical Equations
Isolate the radical, square both sides, solve -- then always check for extraneous solutions.
What You'll Learn
Isolate the radical, then square both sides to remove it.
Solve the resulting equation, which is often linear or quadratic.
Always check every solution in the ORIGINAL equation, not the squared version.
Squaring can introduce extraneous solutions that don't actually satisfy the original.
Example: square root of (2x+3) equals x gives x=3 (valid) and x=-1 (extraneous).
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
Learning resources
Skills
Radical Equations
Square Roots
Extraneous Roots
Quadratic Equations
Factoring
Algebraic Verification
Isolating Variables
NL Curriculum Aligned