Question

What is the simplest form of 2512
?

(2 points)
Responses

25−−√
square root of 25

5
5

12.5
12.5

25−−√12

Answer 1

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:

1. Divide by 2:
\( 2512 \div 2 = 1256 \)
2. Divide by 2 again:
\( 1256 \div 2 = 628 \)
3. Divide by 2 again:
\( 628 \div 2 = 314 \)
4. 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.