Can square pieces of foam board, each with an area of 169 square inches, be cut and used to construct a cube with a volume of 1,728 cubic inches? explain.

No, they cannot.

A square has 4 sides that are equal.  To find the area of a square, we multiply its length and width; since they are the same, we are basically squaring that side. 

A=s²

To find the side if we know the area, we work backward and take the square root:

√169=√s²
13=s

The side length is 13 in.

A cube has the same length, width, and height.  To find the volume of a cube, we multiply these 3 measurements; since they are the same, we are basically cubing the side length:

V=s³

We know the volume is 1728, so we have:

1728=s³

To work backward, we take the cubed root:
∛1728=∛s³
12=s

The side length of the cube would have to be 12; a 13 in side would not work.