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Square Roots and Cube Roots Practice Tests

These Grade 8 Math practice tests cover square roots, cube roots, perfect squares, perfect cubes, radical simplification, estimates, equations, comparisons, and geometry applications.

Skills covered

  • Evaluating principal square roots and cube roots using perfect squares and perfect cubes
  • Locating and estimating radicals with nearby powers and number-line reasoning
  • Simplifying square-root and cube-root expressions while preserving exact values
  • Solving equations such as \(x^2=a\) and \(x^3=a\)
  • Applying roots to area, volume, distance, diagonal, and right-triangle problems

How to use these practice tests

Find nearby perfect squares or cubes first. Then simplify or estimate the radical, check the sign, and square or cube the result to verify it.

For more Grade 8 Math practice, return to the Grade 8 Math category.

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5 Tests
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1. Test

Grade 8 Square Roots and Cube Roots Practice Tests

Practice Grade 8 Math questions about square roots, cube roots, perfect squares, perfect cubes, radical simplification, estimates, equations, and geometry applications.

Choose the best answer for each question. Keep exact radical form when requested and review the explanation after submitting your answers.

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

What does a\sqrt{a} represent for a nonnegative number aa?

Please select an answer first.

Correct answer: A

The correct answer is The nonnegative number whose square is aa.

  1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
  2. Use nearby perfect powers: The principal square root satisfies a≥0\sqrt{a}\ge0 and (a)2=a(\sqrt{a})^2=a.
  3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

The principal square root satisfies a≥0\sqrt{a}\ge0 and (a)2=a(\sqrt{a})^2=a.

2. QuestionMultiple choice

What is the value of 64\sqrt{64}?

Please select an answer first.

Correct answer: B

The correct answer is 88.

  1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
  2. Use nearby perfect powers: 82=648^2=64, so the principal square root of 64 is 8.
  3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

82=648^2=64, so the principal square root of 64 is 8.

3. QuestionMultiple choice

Which number is a perfect square?

Please select an answer first.

Correct answer: C

The correct answer is 8181.

  1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
  2. Use nearby perfect powers: 81=9281=9^2, so 81 has an integer square root.
  3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

81=9281=9^2, so 81 has an integer square root.

4. QuestionMultiple choice

What is the value of 1253\sqrt[3]{125}?

Please select an answer first.

Correct answer: D

The correct answer is 55.

  1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
  2. Use nearby perfect powers: 53=1255^3=125, so the cube root of 125 is 5.
  3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

53=1255^3=125, so the cube root of 125 is 5.

5. QuestionMultiple choice

Which number is a perfect cube?

Please select an answer first.

Correct answer: A

The correct answer is 216216.

  1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
  2. Use nearby perfect powers: 216=63216=6^3, so 216 has an integer cube root.
  3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

216=63216=6^3, so 216 has an integer cube root.

6. QuestionMultiple choice

Between which two integers is 30\sqrt{30}?

Please select an answer first.

Correct answer: B

The correct answer is Between 5 and 6.

  1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
  2. Use nearby perfect powers: Because 52=255^2=25 and 62=366^2=36, 30\sqrt{30} lies between 5 and 6.
  3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

Because 52=255^2=25 and 62=366^2=36, 30\sqrt{30} lies between 5 and 6.

7. QuestionMultiple choice

Between which two integers is 703\sqrt[3]{70}?

Please select an answer first.

Correct answer: C

The correct answer is Between 4 and 5.

  1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
  2. Use nearby perfect powers: Because 43=644^3=64 and 53=1255^3=125, 703\sqrt[3]{70} lies between 4 and 5.
  3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

Because 43=644^3=64 and 53=1255^3=125, 703\sqrt[3]{70} lies between 4 and 5.

8. QuestionMultiple choice

What is the best estimate for 20\sqrt{20}?

Please select an answer first.

Correct answer: D

The correct answer is 4.474.47.

  1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
  2. Use nearby perfect powers: 4.472=19.98094.47^2=19.9809, which is very close to 20.
  3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

4.472=19.98094.47^2=19.9809, which is very close to 20.

9. QuestionMultiple choice

Which is the simplified form of 45\sqrt{45}?

Please select an answer first.

Correct answer: A

The correct answer is 353\sqrt{5}.

  1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
  2. Use nearby perfect powers: 45=9⋅5=35\sqrt{45}=\sqrt{9\cdot5}=3\sqrt{5}.
  3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

45=9⋅5=35\sqrt{45}=\sqrt{9\cdot5}=3\sqrt{5}.

10. QuestionMultiple choice

Which is the simplified form of 543\sqrt[3]{54}?

Please select an answer first.

Correct answer: B

The correct answer is 3233\sqrt[3]{2}.

  1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
  2. Use nearby perfect powers: 543=27⋅23=323\sqrt[3]{54}=\sqrt[3]{27\cdot2}=3\sqrt[3]{2}.
  3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

543=27⋅23=323\sqrt[3]{54}=\sqrt[3]{27\cdot2}=3\sqrt[3]{2}.

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