Square Root Expressions Practice Test

About This "Square Root Expressions Practice Test"

This page moves beyond basic extraction and tests the structure and properties of square-root expressions.

"Perfect-square factors, like radicals, products, quotients, conjugates, variables, domains, principal roots, and nested radicals."

Skills Covered

Perfect-square factors, like radicals, products, quotients, conjugates, variables, domains, principal roots, and nested radicals.

Key Ideas

1. Simplify radicals before combining terms.
2. Only like radicals can be added or subtracted.
3. The principal square root is nonnegative.
4. For real u, √(u²)=|u|.

Common Mistakes to Avoid

Do not distribute a square root over addition, confuse evaluation with ± solutions, or combine unlike radicals.

Practice Format

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