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

1 answer

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

\[ P = 4s \]

where \(s\) is the side length of the square. In this case, the side length \(s\) is \(2\sqrt{12}\).

First, we'll substitute the value of \(s\) into the perimeter formula:

\[ P = 4(2\sqrt{12}) \]

Now calculating this, we first multiply \(4\) by \(2\):

\[ P = 8\sqrt{12} \]

Next, we simplify \(\sqrt{12}\). We can break this down as follows:

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

Now we substitute \(\sqrt{12}\) back into the perimeter expression:

\[ P = 8(2\sqrt{3}) = 16\sqrt{3} \]

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

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