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 \( 3\sqrt{32} \), we can substitute this value into the formula:
\[ \text{Perimeter} = 4 \times 3\sqrt{32} \]
Calculating \( 4 \times 3 \):
\[ 4 \times 3 = 12 \]
Thus, we have:
\[ \text{Perimeter} = 12\sqrt{32} \]
Next, we simplify \( \sqrt{32} \). We can factor \( 32 \) as follows:
\[ 32 = 16 \times 2 = 4^2 \times 2 \]
Taking the square root:
\[ \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2} \]
Now we can substitute \( \sqrt{32} \) back into the expression for the perimeter:
\[ \text{Perimeter} = 12\sqrt{32} = 12 \times 4\sqrt{2} \]
Calculating \( 12 \times 4 \):
\[ 12 \times 4 = 48 \]
Therefore, the perimeter of the square is:
\[ \text{Perimeter} = 48\sqrt{2} \]
Thus, the perimeter of the square in simplest radical form is
\[ \boxed{48\sqrt{2}} \]