Question
Find the perimeter of a square with a side length of 332−−√
. Your answer must be in simplest radical form(1 point)
Responses
163–√
16 square root of 3
12128−−−√
12 square root of 128
1232−−√
12 square root of 32
482–√
48 square root of 2
. Your answer must be in simplest radical form(1 point)
Responses
163–√
16 square root of 3
12128−−−√
12 square root of 128
1232−−√
12 square root of 32
482–√
48 square root of 2
Answers
GPT-4o mini
To find the perimeter of a square, you use the formula:
\[
P = 4s
\]
where \( s \) is the side length of the square. Given that the side length is \( \sqrt{332} \), we substitute this into the formula:
\[
P = 4\sqrt{332}
\]
Next, we simplify \( \sqrt{332} \). First, we find the prime factorization of 332:
\[
332 = 4 \times 83
\]
Now, we can simplify \( \sqrt{332} \):
\[
\sqrt{332} = \sqrt{4 \times 83} = \sqrt{4} \times \sqrt{83} = 2\sqrt{83}
\]
Now substituting back into the perimeter formula:
\[
P = 4 \times 2\sqrt{83} = 8\sqrt{83}
\]
Thus, the perimeter of the square is:
\[
\boxed{8\sqrt{83}}
\]
Please note that none of the options provided in your initial list match the correct answer of \( 8\sqrt{83} \). Make sure to verify the side length or options given, as they may be incorrect.
\[
P = 4s
\]
where \( s \) is the side length of the square. Given that the side length is \( \sqrt{332} \), we substitute this into the formula:
\[
P = 4\sqrt{332}
\]
Next, we simplify \( \sqrt{332} \). First, we find the prime factorization of 332:
\[
332 = 4 \times 83
\]
Now, we can simplify \( \sqrt{332} \):
\[
\sqrt{332} = \sqrt{4 \times 83} = \sqrt{4} \times \sqrt{83} = 2\sqrt{83}
\]
Now substituting back into the perimeter formula:
\[
P = 4 \times 2\sqrt{83} = 8\sqrt{83}
\]
Thus, the perimeter of the square is:
\[
\boxed{8\sqrt{83}}
\]
Please note that none of the options provided in your initial list match the correct answer of \( 8\sqrt{83} \). Make sure to verify the side length or options given, as they may be incorrect.