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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.

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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

Evaluate 81\sqrt{81}

Please select an answer first.

Correct answer: A

The correct answer is 9.

  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: Since 9 squared equals 81, the principal square root of 81 is 9.
  3. Check the value and sign: The correct choice is 9.

Since 9 squared equals 81, the principal square root of 81 is 9.

2. QuestionMultiple choice

Evaluate 121\sqrt{121}

Please select an answer first.

Correct answer: B

The correct answer is 11.

  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: Since 11 squared equals 121, the principal square root is 11.
  3. Check the value and sign: The correct choice is 11.

Since 11 squared equals 121, the principal square root is 11.

3. QuestionMultiple choice

Evaluate 273\sqrt[3]{27}

Please select an answer first.

Correct answer: C

The correct answer is 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: The cube root asks which number cubed equals 27, and 3 cubed is 27.
  3. Check the value and sign: The correct choice is 3.

The cube root asks which number cubed equals 27, and 3 cubed is 27.

4. QuestionMultiple choice

Evaluate −643\sqrt[3]{-64}

Please select an answer first.

Correct answer: D

The correct answer is -4.

  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 cube of -4 is -64, so the real cube root is -4.
  3. Check the value and sign: The correct choice is -4.

The cube of -4 is -64, so the real cube root is -4.

5. QuestionMultiple choice

What is the principal square root of 3636?

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: The principal square root is nonnegative, so sqrt(36) = 6 rather than -6.
  3. Check the value and sign: The correct choice is 6.

The principal square root is nonnegative, so sqrt(36) = 6 rather than -6.

6. QuestionMultiple choice

What is −9\sqrt{-9} in the real number system?

Please select an answer first.

Correct answer: B

The correct answer is It is not a real number..

  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: No real number squared equals -9.
  3. Check the value and sign: The correct choice is It is not a real number..

No real number squared equals -9.

7. QuestionMultiple choice

Solve x2=49x^2=49

Please select an answer first.

Correct answer: C

The correct answer is x = 7 or x = -7.

  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: Both 7 and -7 have square 49, so both are solutions.
  3. Check the value and sign: The correct choice is x = 7 or x = -7.

Both 7 and -7 have square 49, so both are solutions.

8. QuestionMultiple choice

Evaluate 1253\sqrt[3]{125}

Please select an answer first.

Correct answer: D

The correct answer is 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 cube of 5 is 125.
  3. Check the value and sign: The correct choice is 5.

The cube of 5 is 125.

9. QuestionMultiple choice

Evaluate 0\sqrt{0}

Please select an answer first.

Correct answer: A

The correct answer is 0.

  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: Zero squared is zero, so its principal square root is zero.
  3. Check the value and sign: The correct choice is 0.

Zero squared is zero, so its principal square root is zero.

10. QuestionMultiple choice

Between which two consecutive integers does 20\sqrt{20} lie?

Please select an answer first.

Correct answer: B

The correct answer is Between 4 and 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: Because 16 < 20 < 25, sqrt(20) lies between 4 and 5.
  3. Check the value and sign: The correct choice is Between 4 and 5..

Because 16 < 20 < 25, sqrt(20) lies between 4 and 5.

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