Find the perimeter of a square with a side length of 332−−√

. Your answer must be in simplest radical form(1 point)
Responses

482–√
48 square root of 2

1232−−√
12 square root of 32

12128−−−√
12 square root of 128

163–√

1 answer

To find the perimeter of a square, the formula is:

\[ \text{Perimeter} = 4 \times \text{side length} \]

Given the side length of the square is \( \sqrt{332} \), the perimeter can be calculated as follows:

\[ \text{Perimeter} = 4 \times \sqrt{332} \]

We can simplify \( \sqrt{332} \) first:

\[ 332 = 4 \times 83 \]

This means:

\[ \sqrt{332} = \sqrt{4 \times 83} = \sqrt{4} \times \sqrt{83} = 2 \sqrt{83} \]

Now, substituting this back into the perimeter formula:

\[ \text{Perimeter} = 4 \times (2 \sqrt{83}) = 8 \sqrt{83} \]

So the perimeter of the square in simplest radical form is:

\[ 8 \sqrt{83} \]

None of the provided options in your question matches the calculated perimeter of \( 8 \sqrt{83} \). Please check if there was a mistake in the options given or if there's any additional information needed.