Find the perimeter of a square with a side length of 2 square root of 12. Your answer must be in simplest radical form.

1 answer

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

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

Given that the side length of the square is \(2\sqrt{12}\), we'll first simplify \(2\sqrt{12}\).

Starting with \(\sqrt{12}\):

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

Now, substituting this back into the expression for the side length:

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

Now, we can calculate the perimeter:

\[ \text{Perimeter} = 4 \times (4\sqrt{3}) = 16\sqrt{3} \]

Thus, the perimeter of the square is:

\[ \boxed{16\sqrt{3}} \]