Question

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

Note: Put the answer choice in the set that it matches.

Answer 1

Let's analyze each number set to determine the correct description:

a) \( ( \sqrt{25}, 9, \sqrt{64} ) \)
- \( \sqrt{25} = 5 \) (rational)
- \( 9 \) (rational)
- \( \sqrt{64} = 8 \) (rational)
This set contains only rational numbers.
**Answer: 1. Only Rational Numbers**

b) \( ( -2.4, 0, 3.1, \sqrt{81} ) \)
- \( -2.4 \) (rational)
- \( 0 \) (rational)
- \( 3.1 \) (rational)
- \( \sqrt{81} = 9 \) (rational)
This set contains only rational numbers.
**Answer: 1. Only Rational Numbers**

c) \( (-\frac{2}{3}, \frac{7}{9}, \frac{\pi}{2}) \)
- \( -\frac{2}{3} \) (rational)
- \( \frac{7}{9} \) (rational)
- \( \frac{\pi}{2} \) (irrational)
This set contains both rational and irrational numbers.
**Answer: 3. Both Rational & Irrational Numbers**

d) \( (\sqrt{12}, \sqrt{11}, \pi) \)
- \( \sqrt{12} \) (irrational)
- \( \sqrt{11} \) (irrational)
- \( \pi \) (irrational)
This set contains only irrational numbers.
**Answer: 2. Only Irrational Numbers**

So, the answers are:
- a) 1. Only Rational Numbers
- b) 1. Only Rational Numbers
- c) 3. Both Rational & Irrational Numbers
- d) 2. Only Irrational Numbers