Radical Equations Practice Test

About This Radical Equations Practice Test

This test covers equations with one or more radicals, including square roots, cube roots, fourth roots, and equations that create extraneous candidates.

Students must isolate the radical, use an appropriate power, solve the transformed equation, and verify every candidate in the original equation.

Skills Covered

Radical isolation, squaring and cubing, domains, extraneous roots, multiple-radical equations, and no-real-solution conditions.

Key Ideas

1. Isolate a radical before applying a power.
2. A principal square root cannot be negative.
3. Squaring may introduce extra candidates.
4. Always check solutions in the original equation.

Common Mistakes to Avoid

Do not accept every root of the transformed polynomial or square a negative isolated square root as though it were valid.

Practice Format

Each question has four answer choices. The explanation shows the method, completes the algebra, states the conclusion, and explains why every distractor is incorrect.