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

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.

GPT-4o mini · Answer

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: