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
)

responses
only rational numbers
only irrational numbers
both rational and irrational numbers

Answer 1

Let's analyze each set of numbers to determine whether they contain rational numbers, irrational numbers, or both.

a) \((\sqrt{25}, 9, \sqrt{64})\)

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

Description: only rational numbers

b) \((-2.4, 0, 3.1, \sqrt{81})\)

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

Description: only rational numbers

c) \((-23, 79, \pi^2)\)

• \(-23\) (rational)
• \(79\) (rational)
• \(\pi^2\) (irrational)

Description: both rational and irrational numbers

d) \((\sqrt{12}, \sqrt{11}, \pi)\)

• \(\sqrt{12}\) (irrational)
• \(\sqrt{11}\) (irrational)
• \(\pi\) (irrational)

Description: only irrational numbers

Summary of Answers:

a) only rational numbers
b) only rational numbers
c) both rational and irrational numbers
d) only irrational numbers