Find the perimeter of a square with a side length of 3√32. Your answer must be in simplest radical form.
A. 12√32
B. 16√3
C. 48√2
D. 12√128
The perimeter of a square is given by the formula P = 4s, where s is the length of a side of the square.
In this case, the side length is 3√32.
So, the perimeter is P = 4(3√32).
To simplify, we can rewrite 4(3√32) as 12√32.
Next, since the square root of 32 can be simplified further, let's find the prime factors of 32: 2, 2, 2, and 2.
We can group them in pairs: (2 * 2) * (2 * 2).
Taking one 2 from each pair out of the square root, we get 2 * 2 = 4.
Therefore, √32 = 4√2.
Substituting this back into the expression for the perimeter, we have P = 12(4√2) = 48√2.
Therefore, the answer is C. 48√2.