Choose the correct description of the number set.

Number set:

(√2 , √5 , 𝛑 )
(-7.4, 0, 3.232323..., √25 )
(-⅚ , ⅞ , π/2 )
(√8 , √9 , √10 )

Description:

Rational numbers only
Irrational number only
Both rational and irrational

1 answer

Let's analyze each number set to determine if it contains rational or irrational numbers.

  1. Set: \( (\sqrt{2}, \sqrt{5}, \pi) \)

    • \( \sqrt{2} \) and \( \sqrt{5} \) are irrational numbers.
    • \( \pi \) is also an irrational number.
    • Description: Irrational numbers only
  2. Set: \( (-7.4, 0, 3.232323..., \sqrt{25}) \)

    • \(-7.4\) is a rational number.
    • \(0\) is a rational number.
    • \(3.232323...\) (which can be represented as \(3.\overline{23}\)) is a rational number.
    • \( \sqrt{25} = 5 \) is a rational number.
    • Description: Rational numbers only
  3. Set: \( (-\frac{5}{6}, \frac{7}{8}, \frac{\pi}{2}) \)

    • \(-\frac{5}{6}\) and \(\frac{7}{8}\) are rational numbers.
    • \(\frac{\pi}{2}\) is an irrational number (as \(\pi\) is irrational).
    • Description: Both rational and irrational
  4. Set: \( (\sqrt{8}, \sqrt{9}, \sqrt{10}) \)

    • \( \sqrt{8} = 2\sqrt{2} \) is irrational.
    • \( \sqrt{9} = 3 \) is rational.
    • \( \sqrt{10} \) is irrational.
    • Description: Both rational and irrational

Based on this analysis, here is the summary for each set:

  1. \( (\sqrt{2}, \sqrt{5}, \pi) \) - Irrational numbers only
  2. \( (-7.4, 0, 3.232323..., \sqrt{25}) \) - Rational numbers only
  3. \( (-\frac{5}{6}, \frac{7}{8}, \frac{\pi}{2}) \) - Both rational and irrational
  4. \( (\sqrt{8}, \sqrt{9}, \sqrt{10}) \) - Both rational and irrational