Question

Find the perimeter of a square with a side length of 2 square root of 27. Your answer must be in simplest radical form.

Answer 1

To find the perimeter of a square, we use the formula:

\[
P = 4s
\]

where \(s\) is the side length of the square. In this case, the side length \(s\) is given as \(2\sqrt{27}\).

First, let's simplify \(2\sqrt{27}\):

\[
\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}
\]

So, we have:

\[
2\sqrt{27} = 2 \times 3\sqrt{3} = 6\sqrt{3}
\]

Now that we have simplified the side length, we can compute the perimeter:

\[
P = 4s = 4(6\sqrt{3}) = 24\sqrt{3}
\]

Therefore, the perimeter of the square is:

\[
\boxed{24\sqrt{3}}
\]