Given that the surface area of a cube is 384 cm^2

We need to find the length of the side of the cube.

Let us assume that the side is x cm.

Then we know that the area of one of the cube faces is x^2.

But, the cube has 6 faces.

Then the total surface area is given by 6*x^2

But we know that the surface area is 384 cm^2

==> 6x^2 = 384

Now we need to solve for x.

We will divide by 6.

==> x^2 = 384/6 = 64

Now we will take the square root of both sides.

==> x = +- sqrt64 = +-8

But we will ignore -8 because the length can not be negative value.

**Then, the side of the cube is 8 cm.**

A cube has equal sides, with 6 square surfaces. Therefore the area of each square surface is also equal.

So the area each surface = total surface area of the cube/6 = 384 cm^2/6 = 64 cm^2.

Therefore the length side of the the cube = sqrt(64 cm^2) = 8cm.