To simplify \( \sqrt[3]{12513} \), we first determine if \( 12513 \) can be expressed in terms of a factor related to \( 125 \), since \( 125 = 5^3 \).
- Notice that \( 125 = 5^3 \).
- The number \( 12513 \) doesn't appear to be a perfect cube of any integer.
As a result, we will just compute its cube root without further factorization. The options provided in the responses do not contain \( \sqrt[3]{12513} \) directly. Therefore, we should analyze the responses to find the closest:
- \( \sqrt{125} \), which equals \( 5\sqrt{5} \), does not apply because it refers to square roots.
- \( 125^{1/3} \) actually just equals \( 5 \).
- \( \sqrt{125} \) similarly leads to a different number.
Since we are seeking the cube root \( \sqrt[3]{12513} \):
Given that \( 12513 \) does not reduce simply to any of the forms available, the simplest numerical evaluation for the square root or cube root leads us to conclude that none of the responses correctly represent \( 12513 \).
Assuming misunderstandings of how to represent the number; the expected answer might be \( 5 \) from \( \sqrt[3]{125} \), but this does not reflect the cube root of \( 12513 \) accurately.
To summarize: The simplest form for the operation requested would yield an approximate value \( \sqrt[3]{12513} \approx 23.15 \), but such precision was not provided in the prime responses. Hence, among the answers given, \( 5 \) could have been the most relevant in certain contexts, but for correctness regarding \( 12513 \), the remainder of all presented options lack direct relevance.
Thus, the most accurate choice based on your details provided depends critically on your goal; the direct simplification of \( 12513 \) remains unfulfilled properly within the array of potential answers given.
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