Multiplying Radicals Practice Test

About This Multiplying Radicals Practice Test

This set practices multiplication of radicals with equal indices, including numerical radicands, coefficients, and variable expressions. Answers are simplified to exact radical form whenever the radicand is not a perfect power.

Later questions include radical binomials, conjugates, square identities, cube roots, fourth roots, and area applications.

Skills Covered

Using √a·√b = √(ab), multiplying outside coefficients, extracting perfect-square factors, combining like radicals after expansion, and applying conjugate products.

Key Rules

1. Radicals may be combined under one radical when their indices match.
2. Outside coefficients multiply separately from radicands.
3. Always simplify the final radicand by removing perfect powers.
4. Conjugate products eliminate radical middle terms.

Common Mistakes to Avoid

Do not add radicands when multiplying, forget to multiply coefficients, leave a perfect square under the radical, or apply square-root rules to cube roots and fourth roots.

Practice Format

Each explanation shows the exact radical product and explains why the other forms are incomplete or mathematically incorrect.