Question

1. Find the perimeter of a square with a side length of 3√24. Your answer must be in simplest radical form.
24√6
12√128
16√3
12√24

Answer 1

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 \(3\sqrt{24}\), we first calculate the perimeter:

\[
\text{Perimeter} = 4 \times 3\sqrt{24} = 12\sqrt{24}
\]

Next, we can simplify \(\sqrt{24}\):

\[
\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}
\]

Now, substituting this back into the expression for the perimeter:

\[
\text{Perimeter} = 12\sqrt{24} = 12 \times 2\sqrt{6} = 24\sqrt{6}
\]

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

\[
\boxed{24\sqrt{6}}
\]