Select the correct description for each number set.(4 points)

Question

a) (25−−√, 9, −−−√64−−√
)

b) ( -2.4, 0, 3.1, 81−−√
)

c) (−23, 79, π2
)

d) (12−−√, 11−−√, π
)

Answer 1

Let's analyze each number set by identifying the types of numbers contained within them.

a) (25−−√, 9, −−−√64−−√)

• Elements:
  • \( \sqrt{25} = 5 \) (rational number)
  • \( 9 \) (rational number)
  • \( \sqrt{64} = 8 \) (rational number)
• Description: All members of this set are rational numbers.
• Type: Rational Numbers

b) (-2.4, 0, 3.1, 81−−√)

• Elements:
  • \(-2.4\) (rational number)
  • \(0\) (rational number)
  • \(3.1\) (rational number)
  • \( \sqrt{81} = 9 \) (rational number)
• Description: All members of this set are rational numbers.
• Type: Rational Numbers

c) (−23, 79, π2)

• Elements:
  • \(-23\) (integer, hence rational)
  • \(79\) (integer, hence rational)
  • \( \pi^2 \) (irrational number; the square of π is not a rational number)
• Description: This set contains both rational (the integers) and irrational (the \( \pi^2 \)).
• Type: Mixed (Rational and Irrational)

d) (12−−√, 11−−√, π)

• Elements:
  • \( \sqrt{12} \) (irrational number)
  • \( \sqrt{11} \) (irrational number)
  • \( \pi \) (irrational number)
• Description: All members of this set are irrational numbers.
• Type: Irrational Numbers

Final Answer:

a) Rational Numbers
b) Rational Numbers
c) Mixed (Rational and Irrational)
d) Irrational Numbers