Question
What is the simplest form of 2512
?
(1 point)
Responses
25−−√
square root of 25
8
8
5
5
12.5
?
(1 point)
Responses
25−−√
square root of 25
8
8
5
5
12.5
Answers
GPT-4o mini
To simplify 2512, we can first break it down into its prime factors.
The number 2512 can be factored as follows:
2512 = 2 × 1256 = 2 × 2 × 628 = 2 × 2 × 2 × 314 = 2 × 2 × 2 × 2 × 157
The prime factorization of 2512 is \( 2^4 \times 157 \).
Now, we can take the square root of the perfect square part:
\(\sqrt{2512} = \sqrt{2^4 \times 157} = \sqrt{2^4} \times \sqrt{157} = 4\sqrt{157}\).
Now, let's evaluate the options provided:
- \( \sqrt{25} = 5 \)
- \( 8 \) ≠ \( 4\sqrt{157} \)
- \( 5 \) ≠ \( 4\sqrt{157} \)
- \( 12.5 \) ≠ \( 4\sqrt{157} \)
Since none of the responses accurately represent the simplest form of \( 2512 \), we can note that \( 2512 \) in its simplest square root form is \( 4\sqrt{157} \).
However, in terms of a numerical response based on proximity to the choices given:
Checking a numerical approximation of \( 4\sqrt{157} \):
- \( \sqrt{157} \) is approximately \( 12.53 \).
- Thus, \( 4\sqrt{157} \approx 4 \times 12.53 \approx 50.12 \).
None of the responses match that directly.
If I had to choose the closest or a predetermined response likely referring just to integers or multiplication, I would not select any of the given options as they do not represent the square root properly.
The number 2512 can be factored as follows:
2512 = 2 × 1256 = 2 × 2 × 628 = 2 × 2 × 2 × 314 = 2 × 2 × 2 × 2 × 157
The prime factorization of 2512 is \( 2^4 \times 157 \).
Now, we can take the square root of the perfect square part:
\(\sqrt{2512} = \sqrt{2^4 \times 157} = \sqrt{2^4} \times \sqrt{157} = 4\sqrt{157}\).
Now, let's evaluate the options provided:
- \( \sqrt{25} = 5 \)
- \( 8 \) ≠ \( 4\sqrt{157} \)
- \( 5 \) ≠ \( 4\sqrt{157} \)
- \( 12.5 \) ≠ \( 4\sqrt{157} \)
Since none of the responses accurately represent the simplest form of \( 2512 \), we can note that \( 2512 \) in its simplest square root form is \( 4\sqrt{157} \).
However, in terms of a numerical response based on proximity to the choices given:
Checking a numerical approximation of \( 4\sqrt{157} \):
- \( \sqrt{157} \) is approximately \( 12.53 \).
- Thus, \( 4\sqrt{157} \approx 4 \times 12.53 \approx 50.12 \).
None of the responses match that directly.
If I had to choose the closest or a predetermined response likely referring just to integers or multiplication, I would not select any of the given options as they do not represent the square root properly.