To subtract the square roots \( \sqrt{107} - \sqrt{47} \), we can start by simplifying the expression as much as possible.
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Calculate the approximate values of the square roots:
- \( \sqrt{107} \approx 10.34 \)
- \( \sqrt{47} \approx 6.86 \)
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Then compute the difference: \[ \sqrt{107} - \sqrt{47} \approx 10.34 - 6.86 \approx 3.48 \]
Since none of the provided choices correspond directly to a numerical approximation, we'll explore if we can express \( \sqrt{107} - \sqrt{47} \) in a more precise form:
The expression can be left as is: \[ \sqrt{107} - \sqrt{47} \]
Given that this expression doesn't simplify neatly, let’s look at the answer choices:
- \( \sqrt{47} \)
- \( 4\sqrt{7} \)
- \( 67\sqrt{7} \)
- \( 414\sqrt{14} \)
- \( 614 \)
None of these are equivalent to \( \sqrt{107} - \sqrt{47} \). Thus, to stay consistent with the context, it could involve checking numerical differences or closeness to rational approximations.
Given that the common numerical representation does not yield exact simplification, the best rational expression for roots is:
\[ \sqrt{107} - \sqrt{47} \]
In terms of choices, you would have to double-check or provide information on which choice, if any, corresponds closely to a potential numerical solution, but based on the given values, none match neatly.