The simplest form of \( \sqrt{12513} \) cannot be expressed as a simple integer like 5 or the cube root of 125. To find the square root of 12513, we can approximate it:
Calculating:
- \( 125 \) can be factored as \( 5^3 \) and \( 3 \) (since \( 3 \times 5^3 = 125 \)).
- Therefore, \( \sqrt{12513} \) does not simplify nicely by common factors.
- The approximation for \( \sqrt{12513} \) is around \( 111.87 \) since \( 111^2 \approx 12321 \) and \( 112^2 \approx 12544 \).
From the options provided, none seem to simplify correctly, but the numerical approximation \( 41.66 \) does not represent \( \sqrt{12513} \).
So, the best guess is that the question might have intended to ask for \( \sqrt{125} \), which simplifies to \( 5\sqrt{5} \). However, for \( \sqrt{12513} \), it does not have a simple form.
Thus, based on the provided options, the correct answer does not appear to be represented. If you meant \( \sqrt{125} \), then it simplifies to \( 5\sqrt{5} \).
If you are looking specifically for \( \sqrt{12513} \), it remains as it is unless approximated numerically.
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