To simplify 2512, we can break it down into its prime factors.
First, we notice that 2512 can be factored:
2512 = 2 × 1256
1256 = 2 × 628
628 = 2 × 314
314 = 2 × 157
So, the prime factorization of 2512 is \( 2^4 \times 157 \).
Now, to express this in its simplest form, we have \( 2512 = 16 \times 157 \).
If we express it in terms of the square root as per your options, we can consider the square root:
\[ \sqrt{2512} = \sqrt{16 \times 157} = \sqrt{16} \times \sqrt{157} = 4\sqrt{157} \]
However, evaluating the options you provided, none of them seem to reflect this simplification correctly.
The closest interpretation would consider \( 25 \) as a square number, but \( 25 \) wouldn't apply here.
Thus, if we disregard the options related to root forms given and look for clarity, the correct simplest representation of the square root of 2512 would be \( 4\sqrt{157} \), but not listed in your provided options.
If looking strictly at your provided answers, please clarify what you're looking specifically for in those or how you want the expression represented from above.
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