Question

Find the perimeter of a square with a side length of 3√32. Your answer must be in
simplest radical form. (1 point)
12/128
O 12√32
48√2
O 16√3

Answer 1

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

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

Given that the side length of the square is \( 3\sqrt{32} \), we can substitute into the formula:

\[
\text{Perimeter} = 4 \times (3\sqrt{32}) = 12\sqrt{32}
\]

Now, we can simplify \( \sqrt{32} \):

\[
\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}
\]

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

\[
\text{Perimeter} = 12\sqrt{32} = 12 \times 4\sqrt{2} = 48\sqrt{2}
\]

Thus, the perimeter of the square is

\[
\boxed{48\sqrt{2}}
\]