What is the length of each side of a room if it is 784 square feet?

If the floor is a square, then each side of the floor has length square root of 784 which is 28 feet,

That is because:

The area of a square is its length times its width.

A square has all 4 sides the same so its length is the same as its width.

A = l*w

A = l*l because w = l

A = l^2

784 = l^2

sqrt (784) = l

28 = l