Which of the following options includes a rational number and an irrational number between the square root of 6 and the square root of 8?

First, let's find the approximate values of the square roots:

- \(\sqrt{6} \approx 2.449\)
- \(\sqrt{8} \approx 2.828\)

We are looking for a rational number and an irrational number that lie between these two values.

Now let's evaluate the options:

**A. 2.6 as a repeating decimal and the square root of 7**

- \(2.6\) (or \(2.666...\)) is a rational number and it is between \(2.449\) and \(2.828\).
- \(\sqrt{7} \approx 2.645751\), which is also between \(2.449\) and \(2.828\) and is irrational.

**B. 9/4, square root of 7**

- \(9/4 = 2.25\), which is less than \(2.449\).
- \(\sqrt{7} \approx 2.645751\), which is correct.

**C. 2.7, square root of 9**

- \(2.7\) is a rational number and is between \(2.449\) and \(2.828\).
- \(\sqrt{9} = 3\), which is not between \(2.449\) and \(2.828\).

**D. 2.5, pi**

- \(2.5\) is a rational number and is between \(2.449\) and \(2.828\).
- \(\pi \approx 3.14159\), which is greater than \(2.828\).

Among these options, only option A includes both a rational and an irrational number within the range between \(\sqrt{6}\) and \(\sqrt{8}\).

So, the correct answer is **A. 2.6 as a repeating decimal and the square root of 7.**