Question

Which of the following options includes a rational number and an irrational number between √6 and √?(1 point)Responses
2.6¯, √7
2.5, π
9/4, √7
2.7, √9

Answer 1

To identify a pair of one rational number and one irrational number between \(\sqrt{6}\) and \(\sqrt{8}\), let's first calculate these square roots:

- \(\sqrt{6} \approx 2.45\)
- \(\sqrt{8} \approx 2.83\)

So, we need to find numbers between approximately 2.45 and 2.83.

Now let's look at each option:

1. **\(2.6\), \(\sqrt{7}\)**:
- \(2.6\) is rational.
- \(\sqrt{7} \approx 2.645\) (irrational).
- Both numbers are between \( \sqrt{6} \) and \( \sqrt{8} \).

2. **\(2.5\), \(\pi\)**:
- \(2.5\) is rational.
- \(\pi \approx 3.14\) (irrational), but \(\pi\) is not between \(\sqrt{6}\) and \(\sqrt{8}\).

3. **\(9/4\), \(\sqrt{7}\)**:
- \(9/4 = 2.25\) (rational), but it's not between \(\sqrt{6}\) and \(\sqrt{8}\).
- \(\sqrt{7} \approx 2.645\) (irrational), which is fine, but the rational number does not fit.

4. **\(2.7\), \(\sqrt{9}\)**:
- \(2.7\) is rational.
- \(\sqrt{9} = 3\) (irrational), but \(\sqrt{9}\) is not between \(\sqrt{6}\) and \(\sqrt{8}\).

The only option that has both a rational number and an irrational number between \(\sqrt{6}\) and \(\sqrt{8}\) is:

**\(2.6\), \(\sqrt{7}\)**.