NumicornNumicornLearn, solve, progress

Radicals and Real Numbers Practice Tests

These Grade 9 Math practice tests cover rational and irrational numbers, real-number classification, square roots, cube roots, principal roots, radical simplification, combining like radicals, exact and approximate values, rational denominators, Pythagorean applications, and real-number properties.

Skills covered

  • Classifying integers, rational numbers, irrational numbers, and real numbers
  • Evaluating and estimating square roots and cube roots
  • Simplifying, adding, subtracting, multiplying, and dividing radicals
  • Using exact radical forms in distance, diagonal, and right-triangle problems
  • Applying commutative, associative, distributive, identity, inverse, and closure properties

How to use these practice tests

Look for perfect-square or perfect-cube factors, keep the principal square root nonnegative, compare radicals by nearby perfect powers, and preserve exact forms unless a decimal approximation is requested.

For more Grade 9 Math practice, return to the Grade 9 Math category.

Select a test

5 Tests
1. Test2. Test3. Test4. Test5. Test

3. Test

Grade 9 Radicals and Real Numbers Practice Tests

Practice Grade 9 Math questions about rational and irrational numbers, real-number properties, square roots, cube roots, simplifying radicals, exact values, approximations, and applications.

Choose the best answer. Classify the number, preserve exact radical forms when requested, estimate only when appropriate, and check signs and units in applications.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

Simplify 12\sqrt{12}

Please select an answer first.

Correct answer: A

The correct answer is 232\sqrt{3}.

  1. Classify or represent the number: Determine the number set, radical form, exact value, approximation, or property involved.
  2. Apply the radical or real-number rule: Factor 12 as 4 × 3 and take the square root of the perfect square 4.
  3. Check the value and sign: The correct choice is 232\sqrt{3}.

Factor 12 as 4 × 3 and take the square root of the perfect square 4.

2. QuestionMultiple choice

Simplify 18\sqrt{18}

Please select an answer first.

Correct answer: B

The correct answer is 323\sqrt{2}.

  1. Classify or represent the number: Determine the number set, radical form, exact value, approximation, or property involved.
  2. Apply the radical or real-number rule: Factor 18 as 9 × 2, so sqrt(18) = 3sqrt(2).
  3. Check the value and sign: The correct choice is 323\sqrt{2}.

Factor 18 as 9 × 2, so sqrt(18) = 3sqrt(2).

3. QuestionMultiple choice

Simplify 48\sqrt{48}

Please select an answer first.

Correct answer: C

The correct answer is 434\sqrt{3}.

  1. Classify or represent the number: Determine the number set, radical form, exact value, approximation, or property involved.
  2. Apply the radical or real-number rule: Factor 48 as 16 × 3 and take the square root of 16.
  3. Check the value and sign: The correct choice is 434\sqrt{3}.

Factor 48 as 16 × 3 and take the square root of 16.

4. QuestionMultiple choice

Simplify 75\sqrt{75}

Please select an answer first.

Correct answer: D

The correct answer is 535\sqrt{3}.

  1. Classify or represent the number: Determine the number set, radical form, exact value, approximation, or property involved.
  2. Apply the radical or real-number rule: Factor 75 as 25 × 3, so the radical simplifies to 5sqrt(3).
  3. Check the value and sign: The correct choice is 535\sqrt{3}.

Factor 75 as 25 × 3, so the radical simplifies to 5sqrt(3).

5. QuestionMultiple choice

Simplify 72\sqrt{72}

Please select an answer first.

Correct answer: A

The correct answer is 626\sqrt{2}.

  1. Classify or represent the number: Determine the number set, radical form, exact value, approximation, or property involved.
  2. Apply the radical or real-number rule: Factor 72 as 36 × 2 and take the square root of 36.
  3. Check the value and sign: The correct choice is 626\sqrt{2}.

Factor 72 as 36 × 2 and take the square root of 36.

6. QuestionMultiple choice

Simplify 200\sqrt{200}

Please select an answer first.

Correct answer: B

The correct answer is 10210\sqrt{2}.

  1. Classify or represent the number: Determine the number set, radical form, exact value, approximation, or property involved.
  2. Apply the radical or real-number rule: Factor 200 as 100 × 2, giving 10sqrt(2).
  3. Check the value and sign: The correct choice is 10210\sqrt{2}.

Factor 200 as 100 × 2, giving 10sqrt(2).

7. QuestionMultiple choice

Simplify 35+253\sqrt{5}+2\sqrt{5}

Please select an answer first.

Correct answer: C

The correct answer is 555\sqrt{5}.

  1. Classify or represent the number: Determine the number set, radical form, exact value, approximation, or property involved.
  2. Apply the radical or real-number rule: The radicals are like terms, so add their coefficients: 3 + 2 = 5.
  3. Check the value and sign: The correct choice is 555\sqrt{5}.

The radicals are like terms, so add their coefficients: 3 + 2 = 5.

8. QuestionMultiple choice

Simplify 72−327\sqrt{2}-3\sqrt{2}

Please select an answer first.

Correct answer: D

The correct answer is 424\sqrt{2}.

  1. Classify or represent the number: Determine the number set, radical form, exact value, approximation, or property involved.
  2. Apply the radical or real-number rule: Subtract the coefficients of the like radicals: 7 - 3 = 4.
  3. Check the value and sign: The correct choice is 424\sqrt{2}.

Subtract the coefficients of the like radicals: 7 - 3 = 4.

9. QuestionMultiple choice

Simplify 3⋅12\sqrt{3}\cdot\sqrt{12}

Please select an answer first.

Correct answer: A

The correct answer is 6.

  1. Classify or represent the number: Determine the number set, radical form, exact value, approximation, or property involved.
  2. Apply the radical or real-number rule: Multiply inside one radical: sqrt(36) = 6.
  3. Check the value and sign: The correct choice is 6.

Multiply inside one radical: sqrt(36) = 6.

10. QuestionMultiple choice

Simplify 82\frac{\sqrt{8}}{\sqrt{2}}

Please select an answer first.

Correct answer: B

The correct answer is 2.

  1. Classify or represent the number: Determine the number set, radical form, exact value, approximation, or property involved.
  2. Apply the radical or real-number rule: Divide inside the radical: sqrt(8/2) = sqrt(4) = 2.
  3. Check the value and sign: The correct choice is 2.

Divide inside the radical: sqrt(8/2) = sqrt(4) = 2.

Previous testNext test