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Pythagorean Theorem Practice Tests

These Grade 8 Math practice tests cover right triangles, missing side lengths, square roots, exact radical answers, coordinate distance, the converse of the theorem, and real-world applications.

Skills covered

  • Using \(a^2+b^2=c^2\) to find a missing side
  • Identifying the hypotenuse and checking right triangles
  • Simplifying square roots and exact radical expressions
  • Applying the distance formula on the coordinate plane
  • Classifying triangles and solving ramp, ladder, diagonal, and travel problems

How to use these practice tests

Label the hypotenuse first, substitute the known lengths, solve for the missing side, and check that the hypotenuse is the longest side. Keep exact radical forms when a decimal is not requested.

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

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Grade 8 Pythagorean Theorem Practice Tests

Practice Grade 8 Math questions about the Pythagorean Theorem, right triangles, square roots, distance, the converse, and real-world applications.

Choose the best answer for each question. Identify the hypotenuse, use the Pythagorean Theorem, and simplify exact radical answers when needed.

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

What is sqrt25\\sqrt{25}?

Please select an answer first.

Correct answer: A

The correct answer is 55.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The positive number whose square is 25 is 5, so sqrt25=5\\sqrt{25}=5.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The positive number whose square is 25 is 5, so sqrt25=5\\sqrt{25}=5.

2. QuestionMultiple choice

What is sqrt9+16\\sqrt{9+16}?

Please select an answer first.

Correct answer: B

The correct answer is 55.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: First add inside the radical: sqrt9+16=sqrt25=5\\sqrt{9+16}=\\sqrt{25}=5.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

First add inside the radical: sqrt9+16=sqrt25=5\\sqrt{9+16}=\\sqrt{25}=5.

3. QuestionMultiple choice

A right triangle has legs 6 and 8. What is its hypotenuse?

Please select an answer first.

Correct answer: C

The correct answer is 1010.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: Use c=sqrt62+82=sqrt36+64=sqrt100=10c=\\sqrt{6^2+8^2}=\\sqrt{36+64}=\\sqrt{100}=10.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

Use c=sqrt62+82=sqrt36+64=sqrt100=10c=\\sqrt{6^2+8^2}=\\sqrt{36+64}=\\sqrt{100}=10.

4. QuestionMultiple choice

A right triangle has legs 7 and 24. What is its hypotenuse?

Please select an answer first.

Correct answer: D

The correct answer is 2525.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: Use c=sqrt49+576=sqrt625=25c=\\sqrt{49+576}=\\sqrt{625}=25.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

Use c=sqrt49+576=sqrt625=25c=\\sqrt{49+576}=\\sqrt{625}=25.

5. QuestionMultiple choice

A right triangle has hypotenuse 13 and one leg 5. What is the missing leg?

Please select an answer first.

Correct answer: A

The correct answer is 1212.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The missing leg is sqrt132−52=sqrt144=12\\sqrt{13^2-5^2}=\\sqrt{144}=12.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The missing leg is sqrt132−52=sqrt144=12\\sqrt{13^2-5^2}=\\sqrt{144}=12.

6. QuestionMultiple choice

What is the diagonal of a square with side length 6?

Please select an answer first.

Correct answer: B

The correct answer is 6sqrt26\\sqrt{2}.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The diagonal is sqrt62+62=sqrt72=6sqrt2\\sqrt{6^2+6^2}=\\sqrt{72}=6\\sqrt{2}.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The diagonal is sqrt62+62=sqrt72=6sqrt2\\sqrt{6^2+6^2}=\\sqrt{72}=6\\sqrt{2}.

7. QuestionMultiple choice

A rectangle is 9 units by 12 units. What is its diagonal?

Please select an answer first.

Correct answer: C

The correct answer is 1515.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: Use d=sqrt92+122=sqrt225=15d=\\sqrt{9^2+12^2}=\\sqrt{225}=15.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

Use d=sqrt92+122=sqrt225=15d=\\sqrt{9^2+12^2}=\\sqrt{225}=15.

8. QuestionMultiple choice

A 5-foot horizontal distance and a 12-foot vertical distance form a right triangle. What is the diagonal length?

Please select an answer first.

Correct answer: D

The correct answer is 1313 feet.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: Use sqrt52+122=sqrt169=13\\sqrt{5^2+12^2}=\\sqrt{169}=13 feet.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

Use sqrt52+122=sqrt169=13\\sqrt{5^2+12^2}=\\sqrt{169}=13 feet.

9. QuestionMultiple choice

What is sqrt100+100\\sqrt{100+100} in simplest radical form?

Please select an answer first.

Correct answer: A

The correct answer is 10sqrt210\\sqrt{2}.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: Simplify sqrt200=sqrt100cdot2=10sqrt2\\sqrt{200}=\\sqrt{100\\cdot2}=10\\sqrt{2}.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

Simplify sqrt200=sqrt100cdot2=10sqrt2\\sqrt{200}=\\sqrt{100\\cdot2}=10\\sqrt{2}.

10. QuestionMultiple choice

What is sqrt72\\sqrt{72} in simplest radical form?

Please select an answer first.

Correct answer: B

The correct answer is 6sqrt26\\sqrt{2}.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: Factor 72 as 36cdot236\\cdot2, so sqrt72=6sqrt2\\sqrt{72}=6\\sqrt{2}.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

Factor 72 as 36cdot236\\cdot2, so sqrt72=6sqrt2\\sqrt{72}=6\\sqrt{2}.

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