To determine which of the given options is a rational number that comes between \(\sqrt{7}\) and \(\sqrt{8}\), we first need to find approximate values for these square roots:
\[ \sqrt{7} \approx 2.6457513110645906 \quad \text{and} \quad \sqrt{8} \approx 2.8284271247461903. \]
So we are looking for a rational number between \(2.6457513110645906\) and \(2.8284271247461903\).
Now we will evaluate each option:
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\(-\frac{5}{6}\): \[ -\frac{5}{6} \approx -0.8333 \] This number is not between \(\sqrt{7}\) and \(\sqrt{8}\).
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\(-\frac{19}{7}\): \[ -\frac{19}{7} \approx -2.7143 \] This number is also not between \(\sqrt{7}\) and \(\sqrt{8}\).
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\(-\frac{3}{4}\): \[ -\frac{3}{4} \approx -0.75 \] This number is not between \(\sqrt{7}\) and \(\sqrt{8}\).
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\(-\frac{6}{2}\) (which simplifies to \(-3\)): \[ -3 \] This number is not between \(\sqrt{7}\) and \(\sqrt{8}\).
Since none of the options are valid rational numbers that fall between \(\sqrt{7}\) and \(\sqrt{8}\), it appears that none of the provided choices satisfy the condition. Therefore, there is no rational number from the given options that lies between \(\sqrt{7}\) and \(\sqrt{8}\). If you have other numbers or options, feel free to provide those.