Find the perimeter of a square with a side length of 212−−√ . Your answer must be in simplest radical form.(1 point) Responses 323–√ 32 square root of 3 163–√ 16 square root of 3 812−−√ 8 square root of 12 848−−√

Answer 1

To find the perimeter of a square with side length \(\sqrt{212}\), we use the formula for the perimeter of a square, which is:

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

Substituting the given side length:

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

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

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

Substituting this back into the perimeter formula:

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

Thus, the perimeter of the square is:

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