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

1 answer

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.