To determine which option includes a rational number and an irrational number between \( \sqrt{6} \) and \( \sqrt{8} \), we first find the approximate values of these square roots:
- \( \sqrt{6} \) is approximately \( 2.45 \)
- \( \sqrt{8} \) is approximately \( 2.83 \)
Now let's analyze each option:
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2.5, π:
- \( 2.5 \) is rational and \( π \) is irrational.
- \( 2.5 \) is between \( \sqrt{6} \) and \( \sqrt{8} \).
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2.6, \( \sqrt{7} \):
- \( 2.6 \) is rational and \( \sqrt{7} \) is irrational.
- \( 2.6 \) is between \( \sqrt{6} \) and \( \sqrt{8} \) since \( \sqrt{7} \) is also in this range.
-
2.7, \( \sqrt{9} \):
- \( 2.7 \) is rational and \( \sqrt{9} = 3 \) is rational.
- This option does not include an irrational number.
-
94, \( \sqrt{7} \):
- \( 94 \) is rational, but it is not between \( \sqrt{6} \) and \( \sqrt{8} \), and \( \sqrt{7} \) is irrational.
From the analysis above, both options 1 and 2 include one rational and one irrational number that lies between \( \sqrt{6} \) and \( \sqrt{8} \). However, since only one option is typically required in a question like this:
- 2.6, \( \sqrt{7} \) is the best option as both values are also within the specified range.
So the answer could be either option 1 or option 2, but option 2 specifically meets the criteria strictly between \( \sqrt{6} \) and \( \sqrt{8} \) with both types of numbers.
Therefore, the best answer is:
2.6, \( \sqrt{7} \).