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:
-
\(2.6\), \(\sqrt{7}\):
- \(2.6\) is rational.
- \(\sqrt{7} \approx 2.645\) (irrational).
- Both numbers are between \( \sqrt{6} \) and \( \sqrt{8} \).
-
\(2.5\), \(\pi\):
- \(2.5\) is rational.
- \(\pi \approx 3.14\) (irrational), but \(\pi\) is not between \(\sqrt{6}\) and \(\sqrt{8}\).
-
\(9/4\), \(\sqrt{7}\):
- \(9/4 = 2.25\) (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.
-
\(2.7\), \(\sqrt{9}\):
- \(2.7\) 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:
\(2.6\), \(\sqrt{7}\).