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–√
32 square root of 3
163–√
16 square root of 3
812−−√
8 square root of 12
848−−√
. 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−−√
Answers
Answered by
GPT-4o mini
To find the perimeter of a square, you can use the formula:
\[
\text{Perimeter} = 4 \times \text{side length}
\]
Given the side length of the square is \( \sqrt{212} \):
\[
\text{Perimeter} = 4 \times \sqrt{212}
\]
Now, let's simplify \( \sqrt{212} \):
\[
\sqrt{212} = \sqrt{4 \times 53} = \sqrt{4} \times \sqrt{53} = 2\sqrt{53}
\]
Now substituting this back into the perimeter calculation:
\[
\text{Perimeter} = 4 \times (2\sqrt{53}) = 8\sqrt{53}
\]
Thus, the perimeter of the square in simplest radical form is:
\[
\boxed{8\sqrt{53}}
\]
Regarding the given options, there does not seem to be a direct match to our answer, but the perimeter we calculated is indeed \(8\sqrt{53}\). Please provide clarity on the comparison of our answer with the provided choices.
\[
\text{Perimeter} = 4 \times \text{side length}
\]
Given the side length of the square is \( \sqrt{212} \):
\[
\text{Perimeter} = 4 \times \sqrt{212}
\]
Now, let's simplify \( \sqrt{212} \):
\[
\sqrt{212} = \sqrt{4 \times 53} = \sqrt{4} \times \sqrt{53} = 2\sqrt{53}
\]
Now substituting this back into the perimeter calculation:
\[
\text{Perimeter} = 4 \times (2\sqrt{53}) = 8\sqrt{53}
\]
Thus, the perimeter of the square in simplest radical form is:
\[
\boxed{8\sqrt{53}}
\]
Regarding the given options, there does not seem to be a direct match to our answer, but the perimeter we calculated is indeed \(8\sqrt{53}\). Please provide clarity on the comparison of our answer with the provided choices.