To simplify the square root of 2512, we can factor it to see if there are any perfect squares.
First, let's find the prime factorization of 2512:
- Divide by 2:
\( 2512 \div 2 = 1256 \) - Divide by 2 again:
\( 1256 \div 2 = 628 \) - Divide by 2 again:
\( 628 \div 2 = 314 \) - Divide by 2 again:
\( 314 \div 2 = 157 \) (which is a prime number)
So, the prime factorization of 2512 is:
\( 2512 = 2^4 \times 157 \)
Now, we can simplify \( \sqrt{2512} \):
\[ \sqrt{2512} = \sqrt{2^4 \times 157} = \sqrt{2^4} \times \sqrt{157} = 4\sqrt{157} \]
Thus, the simplest form of \( \sqrt{2512} \) is \( 4\sqrt{157} \).
Among the given responses, none match the simplest form of \( \sqrt{2512} \), but this result can be used as an answer if needed in further questions.