Question

Find the perimeter of a square with a side length of 212−−√
. Your answer must be in simplest radical form.(1 point)
Responses

323–√

163–√

812−−√

848−−√

Answer 1

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

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

Given that the side length of the square is \( \sqrt{212} \), we can substitute this into the formula:

\[
\text{Perimeter} = 4 \times \sqrt{212}
\]

Now we can simplify \( \sqrt{212} \):

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

Now, substituting this back into the perimeter formula:

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

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

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