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