Question

Find the perimeter of a square with a side length of 2 and the square root of 12. Your answer must be in simplest radical form.(1 point) Responses

Answer 1

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 \(2 + \sqrt{12}\), we first simplify \(\sqrt{12}\):

\[
\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}
\]

Now, we can express the side length as follows:

\[
\text{side length} = 2 + 2\sqrt{3}
\]

Now we can calculate the perimeter:

\[
\text{Perimeter} = 4 \times (2 + 2\sqrt{3}) = 4 \times 2 + 4 \times 2\sqrt{3} = 8 + 8\sqrt{3}
\]

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

\[
\boxed{8 + 8\sqrt{3}}
\]