Question

Find the perimeter of a square with a side length of 3⎷32. your answer must be in the simplest radical form (1 point)

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 first calculate the perimeter:

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

Next, we simplify \( \sqrt{32} \).

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

Now substitute this back into the perimeter calculation:

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

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

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