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

Solving equations with one radical by isolating and squaring

Solving equations with two radicals by separating them before squaring

Factoring quadratic equations that result from squaring radical expressions

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:

Converting radicals to entire radicals Adding and subtracting radicals Multiplying and dividing radicals Rationalize the denominator

This Unit Includes

8 Video lessons

Practice exercises

Skills

Radical Equations

Square Roots

Extraneous Roots

Quadratic Equations

Factoring

Algebraic Verification

Isolating Variables