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

Question

a) (25−−√, 9, −−−√64−−√
)

b) ( -2.4, 0, 3.1, 81−−√
)

c) (−2/3, 7/9, π/2
)

d) (12−−√, 11−−√, π
)
The answer choices are: 1. Only Rational Numbers 2. Only Irrational Numbers 3. Both Rational & Irrational Numbers, put the correct shoice in the set that it belongs in.

Answer 1

Let's analyze each set individually:

a) The set \( (25^{1/2}, 9, \sqrt{64}) \)

• \( 25^{1/2} = 5 \) (rational)
• \( 9 \) (rational)
• \( \sqrt{64} = 8 \) (rational) This set contains only rational numbers. Choice: 1. Only Rational Numbers

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

• \( -2.4 \) (rational)
• \( 0 \) (rational)
• \( 3.1 \) (rational)
• \( \sqrt{81} = 9 \) (rational) This set also contains only rational numbers. Choice: 1. Only Rational Numbers

c) The set \( (-2/3, 7/9, \pi/2) \)

• \( -2/3 \) (rational)
• \( 7/9 \) (rational)
• \( \pi/2 \) (irrational; as it is a multiple of an irrational number) This set contains both rational and irrational numbers. Choice: 3. Both Rational & Irrational Numbers

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

• \( \sqrt{12} \) (irrational)
• \( \sqrt{11} \) (irrational)
• \( \pi \) (irrational) This set contains only irrational numbers. Choice: 2. Only Irrational Numbers

Here's the summary of choices for each set:

• a) 1. Only Rational Numbers
• b) 1. Only Rational Numbers
• c) 3. Both Rational & Irrational Numbers
• d) 2. Only Irrational Numbers