Question

Which of the following options includes a rational number and an irrational number between 6–√
and 8–√
?(1 point)
Responses

2.7, 9–√
2.7, 9–√
- no response given

2.5, π
2.5, π
- no response given

94, 7–√
94, 7–√
- incorrect

2.6¯¯¯, 7–√

Answer 1

To determine which of the provided options includes a rational number and an irrational number between \( 6 - \sqrt{} \) and \( 8 - \sqrt{} \), let's first clarify the notation:

- \( 6 - \sqrt{} \) is likely a shorthand for \( 6 - \sqrt{n} \) where \( n \) is some integer or expression.
- Similarly, \( 8 - \sqrt{} \) would be \( 8 - \sqrt{m} \).

Since the specific values of \( n \) and \( m \) are not provided, let's interpret \( 6 - \sqrt{} \) and \( 8 - \sqrt{} \) to represent numbers that can be evaluated based on the context of the options.

Looking at the options:
1. **2.7, 9–√**
- 2.7 is a rational number.
- \( \sqrt{9} = 3 \), which is a rational number as well, so this option is not valid.

2. **2.5, π**
- 2.5 is a rational number.
- π (pi) is an irrational number. So this option is valid.

3. **94, 7–√**
- 94 is a rational number.
- \( \sqrt{7} \) is an irrational number, but the lower end \( 6 - \sqrt{7} \) doesn't fit the constraints provided, so this option is not valid.

4. **2.6¯¯¯, 7–√**
- \( 2.6¯¯¯ \) (which we can interpret as 2.666...) is still a rational number.
- \( \sqrt{7} \) is an irrational number. Similar to the previous choice, the range does not meet the criteria.

The only valid option that includes a rational number and an irrational number within the specified bounds is **2.5, π**.