Adding and Subtracting Radicals Practice Test

About This Adding and Subtracting Radicals Practice Test

This test concentrates on one essential radical skill: simplify each square root completely, identify terms with the same square-free radicand, and then add or subtract their coefficients. The 20 questions range from already-matching radicals to expressions where every term must first be rewritten.

The practice also includes variables under square roots, a geometric perimeter problem, recognition of unlike radicals, and correction of the false rule that square roots can be added by adding their radicands.

Skills Practiced

• Finding the largest perfect-square factor of a radicand.
• Rewriting radicals in simplest form.
• Combining coefficients of like radicals.
• Leaving unlike radicals as separate terms.
• Using exact radical values in a short application.

A Reliable Simplification Routine

1. Simplify every radical separately.
2. Multiply any coefficient outside the radical.
3. Group terms with identical simplified radicands.
4. Add or subtract only their coefficients.
5. Check that no perfect-square factor remains inside a square root.

Common Errors

The identity $\sqrt{a}+\sqrt{b}\ne \sqrt{a+b}$ is central to this topic. Other common mistakes include forgetting an outside coefficient, stopping before a radical is fully simplified, and combining terms whose square-free radicands are different.

Practice Format

Every problem provides immediate feedback and an exact-form explanation. The final result is based on all 20 questions, so unanswered items are counted as skipped.