Math Problem Statement

Classify the given numbers as either rational or irrational.

Solution

The image shows a table where you need to classify numbers as either rational or irrational. Let's analyze each number:

  1. 64\sqrt{64}:

    • 64=8\sqrt{64} = 8, which is an integer. Integers are rational numbers.
    • Classification: Rational
  2. 85.11-85.11:

    • 85.11-85.11 is a terminating decimal, which can be expressed as a fraction. Therefore, it is a rational number.
    • Classification: Rational
  3. 7-\sqrt{7}:

    • 7\sqrt{7} is not a perfect square, so it is an irrational number. The negative sign does not affect the irrationality.
    • Classification: Irrational
  4. 54.154.\overline{1}:

    • 54.154.\overline{1} represents a repeating decimal (54.1111...), which can be expressed as a fraction. Repeating decimals are rational numbers.
    • Classification: Rational
  5. 14π14\pi:

    • π\pi is an irrational number, and multiplying it by any non-zero rational number (such as 14) still results in an irrational number.
    • Classification: Irrational

Final Table:

NumberRationalIrrational
64\sqrt{64}
85.11-85.11
7-\sqrt{7}
54.154.\overline{1}
14π14\pi

Would you like further details on any of these concepts?

Here are some related questions you might be interested in:

  1. What makes a number rational or irrational?
  2. How do you convert a repeating decimal into a fraction?
  3. Can irrational numbers ever be written as fractions?
  4. What are some other examples of irrational numbers?
  5. How does the square root of a non-perfect square differ from that of a perfect square?

Tip: Remember, a terminating or repeating decimal is always rational!

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Math Problem Analysis

Mathematical Concepts

Number Classification
Rational Numbers
Irrational Numbers

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8