To find a possible value of \( m \) satisfying the inequality \( \sqrt{8} < m < \sqrt{5} \), we first calculate the values of \( \sqrt{8} \) and \( \sqrt{5} \).
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\( \sqrt{8} \) can be simplified as follows: \[ \sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \approx 2 \cdot 1.414 \approx 2.828 \]
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\( \sqrt{5} \) can be approximated as: \[ \sqrt{5} \approx 2.236 \]
Now we have the inequality: \[ 2.828 < m < 2.236 \]
However, there seems to be an issue because \( \sqrt{8} \) (approximately 2.828) is greater than \( \sqrt{5} \) (approximately 2.236). This means that the inequality \( \sqrt{8} < m < \sqrt{5} \) cannot be satisfied since no value of \( m \) can simultaneously be greater than 2.828 and less than 2.236.
Thus, there are no possible values for \( m \) that satisfy the given inequality.