Determine whether each statement below is true or false.(5 points)

Question

True False
23 is a rational number.

-9 is a whole number.

0 is a natural number.

64−−√ is a rational number.

π is an irrational number.

Answer 1

Let's evaluate each statement:

1. 23 is a rational number.
   True - A rational number is any number that can be expressed as a fraction of two integers. Since 23 can be expressed as \( \frac{23}{1} \), it is a rational number.

2. -9 is a whole number.
   False - Whole numbers are the set of non-negative integers (0, 1, 2, 3, ...). Since -9 is negative, it is not a whole number.

3. 0 is a natural number.
   False - Natural numbers are typically defined as the set of positive integers starting from 1 (1, 2, 3, ...). However, some definitions include 0 in the set of natural numbers. In standard definitions, 0 is not considered a natural number.

4. \(\sqrt{64}\) is a rational number.
   True - \(\sqrt{64} = 8\), which is a whole number and hence also a rational number.

5. π is an irrational number.
   True - π (pi) is known to be an irrational number because it cannot be expressed as a fraction of two integers.

To summarize:

1. True
2. False
3. False
4. True
5. True