Question

Find the perimeter of a square with a side length of 212−−√ . Your answer must be in simplest radical form.(1 point) Responses 848−−√ 8 square root of 48 323–√ 32 square root of 3 163–√ 16 square root of 3 812−−√

Answer 1

To find the perimeter \( P \) of a square, you can use the formula:

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

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

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

Next, simplify \( \sqrt{212} \). We can factor \( 212 \) into its prime components:

\[
212 = 4 \times 53
\]

Now, we can take the square root:

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

Now substitute \( 2\sqrt{53} \) back into the perimeter formula:

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

Thus, the perimeter of the square is:

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