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

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