Question

Find the perimeter of a square with a side length of 212−−√212 . Your answer must be in simplest radical form.(1 point) Responses 323–√32332 square root of 3 812−−√8128 square root of 12 848−−√8488 square root of 48 163–√

Answer 1

To find the perimeter of a square, you can use the formula:

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

In this case, the side length is \( \sqrt{212} \). Therefore, the perimeter \( P \) can be calculated as:

\[
P = 4 \times \sqrt{212}
\]

Now, let's simplify \( \sqrt{212} \):

\[
\sqrt{212} = \sqrt{4 \times 53} = \sqrt{4} \times \sqrt{53} = 2\sqrt{53}
\]

Now substitute this back into the perimeter formula:

\[
P = 4 \times 2\sqrt{53} = 8\sqrt{53}
\]

Thus, the perimeter of the square is \( 8\sqrt{53} \).

Since the question requests the answer in simplest radical form, the final answer is:

\[
\boxed{8\sqrt{53}}
\]