To find a rational number between \( \sqrt{10} \) and \( \sqrt{11} \), we can first approximate the square roots:
\[ \sqrt{10} \approx 3.16 \] \[ \sqrt{11} \approx 3.32 \]
Thus, we're looking for a rational number between approximately 3.16 and 3.32.
Now, let's evaluate the given options:
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3.4: This is greater than 3.32, so it is not between \( \sqrt{10} \) and \( \sqrt{11} \).
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3.1: This is less than 3.16, so it is not between \( \sqrt{10} \) and \( \sqrt{11} \).
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16/5: This equals \( 3.2 \), which is between 3.16 and 3.32.
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10/3: This equals approximately \( 3.33 \), which is greater than \( \sqrt{11} \).
From the possibilities given, 16/5 (which is equal to 3.2) is the only rational number that lies between \( \sqrt{10} \) and \( \sqrt{11} \).
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