Math Problem Statement

Classify the numbers √6, −51/5, √64, and 9.68 as rational or irrational.

Solution

The image you’ve uploaded contains a table asking to classify numbers as either rational or irrational. Let’s analyze each number:

  1. √6:

    • The square root of 6 is not a perfect square, and its decimal form is non-terminating and non-repeating. Therefore, √6 is irrational.
  2. −51/5:

    • This is a fraction, and any fraction where both the numerator and denominator are integers is rational. So, −51/5 is rational.
  3. √64:

    • The square root of 64 is 8 (since 64 is a perfect square). Since 8 is an integer, √64 is rational.
  4. 9.68:

    • 9.68 is a terminating decimal, and any terminating decimal is rational.

Final classification:

  • √6: Irrational
  • −51/5: Rational
  • √64: Rational
  • 9.68: Rational

Would you like more details on any of these?

Here are 5 related questions for further exploration:

  1. What makes a number irrational?
  2. Can a square root of a number ever be irrational?
  3. Why are terminating decimals always rational?
  4. What is the difference between repeating and non-repeating decimals in terms of rationality?
  5. Can a negative fraction ever be irrational?

Tip: A good way to remember rational numbers is that they can always be expressed as a fraction of two integers.

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Math Problem Analysis

Mathematical Concepts

Number Classification
Rational Numbers
Irrational Numbers
Square Roots
Decimals

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8