To find a rational number between \(\sqrt{6}\) and \(\sqrt{8}\), we first need to calculate the approximate values of these square roots:
- \(\sqrt{6} \approx 2.449\)
- \(\sqrt{8} \approx 2.828\)
Next, we can look for a rational number that lies between these two values. A simple rational number that fits this range is \(2.5\) (which can be expressed as the fraction \(\frac{5}{2}\)).
Thus, we have found a rational number between \(\sqrt{6}\) and \(\sqrt{8}\):
\[ \frac{5}{2} = 2.5 \]
You can also find other rational numbers in this range, like \(2.6\), \(2.7\), or \(2.75\), etc. Any number in this range that can be expressed as a fraction of two integers will be a rational number between \(\sqrt{6}\) and \(\sqrt{8}\).
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