Rational And Irratonal Square Roots

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| By Carlosvaras
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Carlosvaras
Community Contributor
Quizzes Created: 1 | Total Attempts: 242
Questions: 10 | Attempts: 243

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Rational Quizzes & Trivia

Please answer true or false to the statement.


Questions and Answers
  • 1. 

    The square root of 64 is irrational.

    • A.

      True

    • B.

      False

    Correct Answer
    B. False
    Explanation
    The square root of 64 is not irrational. The square root of 64 is 8, which is a rational number because it can be expressed as a fraction (8/1). Irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal representations. Since 8 can be expressed as a fraction and has a terminating decimal representation, it is not irrational. Therefore, the correct answer is false.

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  • 2. 

    The square root of 34.6 is rational.

    • A.

      True

    • B.

      False

    Correct Answer
    B. False
    Explanation
    The square root of 34.6 is not rational because it cannot be expressed as a fraction of two integers. The square root of 34.6 is an irrational number, meaning it goes on infinitely without repeating and cannot be expressed as a simple fraction.

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  • 3. 

    The square root of 36 is rational.

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    The square root of 36 is rational because it equals 6, which is a whole number and can be expressed as a ratio of two integers. In this case, 6 can be written as 6/1, making it a rational number.

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  • 4. 

    The square root of 81 is rational.

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    The square root of 81 is rational because 81 is a perfect square. The square root of a perfect square is always a whole number, and whole numbers are considered rational numbers. In this case, the square root of 81 is 9, which is a whole number and therefore rational.

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  • 5. 

    The square root of 82 is rational.

    • A.

      True

    • B.

      False

    Correct Answer
    B. False
    Explanation
    The square root of 82 is not rational because it cannot be expressed as a fraction of two integers. The square root of 82 is an irrational number, which means it cannot be written as a terminating or repeating decimal. Therefore, the correct answer is False.

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  • 6. 

    The square root of 72.6 is irrational.

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    The square root of 72.6 is irrational because it cannot be expressed as a fraction or a terminating or repeating decimal. The decimal representation of the square root of 72.6 goes on indefinitely without repeating, indicating that it is an irrational number.

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  • 7. 

    The square root of 25 is rational.

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    The square root of 25 is rational because a rational number is any number that can be expressed as a fraction of two integers. In this case, the square root of 25 is 5, which can be expressed as the fraction 5/1. Therefore, it is rational.

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  • 8. 

    The square root of 50 is irrational.

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    The square root of 50 is irrational because it cannot be expressed as a fraction or a terminating or repeating decimal. It is a non-repeating, non-terminating decimal. The square root of 50 can be simplified as the square root of 25 times the square root of 2, which is 5 times the square root of 2. Since the square root of 2 is irrational, the square root of 50 is also irrational.

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  • 9. 

    The square root of 100 is irrational.

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    The square root of 100 is irrational because it cannot be expressed as a fraction or a terminating or repeating decimal. The square root of 100 is 10, which is a rational number, but it is also -10, which is also a rational number. Therefore, the square root of 100 has two rational solutions, making it irrational.

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  • 10. 

    The square root of 49 is irrational.

    • A.

      True

    • B.

      False

    Correct Answer
    B. False
    Explanation
    The square root of 49 is not irrational because it is equal to 7, which is a rational number.

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  • Current Version
  • Mar 21, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Oct 04, 2013
    Quiz Created by
    Carlosvaras
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