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:
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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.
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2.5, π
- 2.5 is a rational number.
- π (pi) is an irrational number. So this option is valid.
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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.
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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.