Which of the following options includes a rational number and an irrational number between 6–√

Question

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.