Question

Select the correct description for each number set.(4 points)c) (−23, 79, π2)
d) (12−−√, 11−−√, π)
b( -2.4, 0, 3.1, 81−−√)
a) (25−−√, 9, −−−√64−−√)

Answer 1

To determine the correct descriptions for each number set, let's analyze each one:

a) \( (\sqrt{25}, 9, \sqrt[3]{64}) \)

- \( \sqrt{25} = 5 \)
- \( 9 \) is a whole number.
- \( \sqrt[3]{64} = 4 \)

All values are rational numbers. This set is classified as **rational numbers**.

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

- \( -2.4 \) is a rational number.
- \( 0 \) is a rational number.
- \( 3.1 \) is a rational number.
- \( \sqrt{81} = 9 \) is a rational number.

All values are rational numbers. This set is classified as **rational numbers**.

c) \( (-23, 79, \pi^2) \)

- \( -23 \) is an integer (and thus a rational number).
- \( 79 \) is also an integer (and thus a rational number).
- \( \pi^2 \) is an irrational number (since \( \pi \) is irrational).

This set contains both rational and irrational numbers. It can be classified as a **mixed set** of rational and irrational numbers.

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

- \( \sqrt{12} \) is irrational (it cannot be expressed as a fraction).
- \( \sqrt{11} \) is also irrational.
- \( \pi \) is irrational.

All values are irrational numbers. This set is classified as **irrational numbers**.

To summarize the descriptions:
- a) Rational numbers
- b) Rational numbers
- c) Mixed set of rational and irrational numbers
- d) Irrational numbers