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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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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 is the value of 121\sqrt{121}?

Please select an answer first.

Correct answer: A

The correct answer is 1111.

  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: 112=12111^2=121, so the principal square root is 11.
  3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

112=12111^2=121, so the principal square root is 11.

2. QuestionMultiple choice

What is the value of 144\sqrt{144}?

Please select an answer first.

Correct answer: B

The correct answer is 1212.

  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: 122=14412^2=144, so 144=12\sqrt{144}=12.
  3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

122=14412^2=144, so 144=12\sqrt{144}=12.

3. QuestionMultiple choice

What is the value of −83\sqrt[3]{-8}?

Please select an answer first.

Correct answer: C

The correct answer is −2-2.

  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: (−2)3=−8(-2)^3=-8, so the cube root of -8 is -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.

(−2)3=−8(-2)^3=-8, so the cube root of -8 is -2.

4. QuestionMultiple choice

Which statement about square roots is true?

Please select an answer first.

Correct answer: D

The correct answer is The principal square root of a positive number is positive..

  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 is defined as the nonnegative root; for a positive radicand, it is positive.
  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 is defined as the nonnegative root; for a positive radicand, it is positive.

5. QuestionMultiple choice

Which is the simplified form of 75\sqrt{75}?

Please select an answer first.

Correct answer: A

The correct answer is 535\sqrt{3}.

  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: 75=25⋅3=53\sqrt{75}=\sqrt{25\cdot3}=5\sqrt{3}.
  3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

75=25⋅3=53\sqrt{75}=\sqrt{25\cdot3}=5\sqrt{3}.

6. QuestionMultiple choice

Which is the simplified form of 98\sqrt{98}?

Please select an answer first.

Correct answer: B

The correct answer is 727\sqrt{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: 98=49⋅2=72\sqrt{98}=\sqrt{49\cdot2}=7\sqrt{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.

98=49⋅2=72\sqrt{98}=\sqrt{49\cdot2}=7\sqrt{2}.

7. QuestionMultiple choice

Which is the simplified form of 48\sqrt{48}?

Please select an answer first.

Correct answer: C

The correct answer is 434\sqrt{3}.

  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: 48=16⋅3=43\sqrt{48}=\sqrt{16\cdot3}=4\sqrt{3}.
  3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

48=16⋅3=43\sqrt{48}=\sqrt{16\cdot3}=4\sqrt{3}.

8. QuestionMultiple choice

Which is the simplified form of 243\sqrt[3]{24}?

Please select an answer first.

Correct answer: D

The correct answer is 2332\sqrt[3]{3}.

  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: 243=8⋅33=233\sqrt[3]{24}=\sqrt[3]{8\cdot3}=2\sqrt[3]{3}.
  3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

243=8⋅33=233\sqrt[3]{24}=\sqrt[3]{8\cdot3}=2\sqrt[3]{3}.

9. QuestionMultiple choice

Which comparison is true?

Please select an answer first.

Correct answer: A

The correct answer is 12>3.4\sqrt{12}>3.4.

  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: 12≈3.464\sqrt{12}\approx3.464, which is greater than 3.4.
  3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

12≈3.464\sqrt{12}\approx3.464, which is greater than 3.4.

10. QuestionMultiple choice

Which comparison is true?

Please select an answer first.

Correct answer: B

The correct answer is 303<3.2\sqrt[3]{30}<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: 303≈3.107\sqrt[3]{30}\approx3.107, which is less than 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.

303≈3.107\sqrt[3]{30}\approx3.107, which is less than 3.2.

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