Question

Find the perimeter of a square with a side length of 332−−√
. Your answer must be in simplest radical form.(1 point)
Responses

246–√
24 square root of 6

12128−−−√
12 square root of 128

163–√
16 square root of 3

1224−−√

Answer 1

The perimeter \( P \) of a square with side length \( s \) is calculated using the formula:

\[
P = 4s
\]

In this case, the side length is \( s = \sqrt{332} \). Thus, we can calculate the perimeter as follows:

\[
P = 4 \sqrt{332}
\]

Next, we simplify \( \sqrt{332} \). We can factor 332:

\[
332 = 4 \times 83
\]

Now, taking the square root:

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

Substituting this back into the formula for the perimeter:

\[
P = 4(2\sqrt{83}) = 8\sqrt{83}
\]

Thus, the perimeter of the square, in simplest radical form, is:

\[
\boxed{8\sqrt{83}}
\]

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