Which numbers are rational? Check the three that apply.

Question

Responses

\/104

pi

\/16

\/21

7/23

3.8

Answer 1

To determine which numbers are rational, recall that a rational number is any number that can be expressed as the quotient or fraction \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).

Now, let's evaluate the given options:

1. \( \sqrt{104} \): This is an irrational number because it cannot be simplified into a fraction of two integers.

2. \( \pi \): This is also an irrational number and cannot be expressed as a fraction.

3. \( \sqrt{16} \): This simplifies to 4, a whole number, which is rational (since it can be expressed as \( \frac{4}{1} \)).

4. \( \sqrt{21} \): This is an irrational number because it cannot be simplified into a fraction of two integers.

5. \( \frac{7}{23} \): This is a fraction of two integers, making it a rational number.

6. 3.8: This can be expressed as \( \frac{38}{10} \) or \( \frac{19}{5} \), thus it is also a rational number.

The three numbers that are rational from the given options are:

• \( \sqrt{16} \)
• \( \frac{7}{23} \)
• 3.8