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Is each number rational or irrational?



Select Rational or Irrational for each number.

Rational Irrational
0.5

24−−√

3.42859873

64−−√3

1 answer

Let's evaluate each of the numbers:

  1. 0.5: This is a decimal representation of the fraction \( \frac{1}{2} \), which is a rational number.

    • Answer: Rational

  2. \( \sqrt{24} \): This can be simplified to \( \sqrt{4 \cdot 6} = 2\sqrt{6} \). Since \( \sqrt{6} \) is an irrational number, \( 2\sqrt{6} \) is also irrational.

    • Answer: Irrational

  3. 3.42859873: This is a finite decimal, which can be expressed as a fraction. Therefore, it is a rational number.

    • Answer: Rational

  4. \( 64\sqrt{3} \): The number \( \sqrt{3} \) is irrational, and multiplying it by 64 (a rational number) keeps it irrational.

    • Answer: Irrational

So the classifications are:

  • 0.5: Rational
  • \( \sqrt{24} \): Irrational
  • 3.42859873: Rational
  • \( 64\sqrt{3} \): Irrational