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Select the correct description for each number set. Rational, Irrational, or both?

(25−−√, 9, −−−√64−−√)

( -2.4, 0, 3.1, 81−−√)

(−23, 79, π2)

(12−−√, 11−−√, π)

1 answer

Let's analyze each set of numbers to determine whether each number is rational, irrational, or both:

  1. Set: \( (\sqrt{25}, 9, \sqrt{64}) \)

    • \(\sqrt{25} = 5\) (rational)
    • \(9\) (rational)
    • \(\sqrt{64} = 8\) (rational)
      Description: Rational

  2. Set: \( (-2.4, 0, 3.1, \sqrt{81}) \)

    • \(-2.4\) (rational)
    • \(0\) (rational)
    • \(3.1\) (rational)
    • \(\sqrt{81} = 9\) (rational)
      Description: Rational

  3. Set: \( (-23, 79, \pi^2) \)

    • \(-23\) (rational)
    • \(79\) (rational)
    • \(\pi^2\) (irrational, because \(\pi\) is irrational and the square of an irrational number is also irrational)
      Description: Both (since there are both rational and irrational numbers in the set)

  4. Set: \( (\sqrt{12}, \sqrt{11}, \pi) \)

    • \(\sqrt{12}\) (irrational, can be simplified to \(2\sqrt{3}\))
    • \(\sqrt{11}\) (irrational)
    • \(\pi\) (irrational)
      Description: Irrational

Summary of Descriptions:

  1. Rational
  2. Rational
  3. Both
  4. Irrational