Question

For his architecture class, Adam designs the floor of a building as an exact square. If the length of each side of the square floor is a natural number measured in feet, which one of the following cannot be its area?

• A. 4337 sq ft
• B. 7225 sq ft
• C. 3249 sq ft
• D. 5776 sq ft

Answer 1

The correct option is A 4337 sq ft

As the side length of the square floor is a natural number measured in feet, its area will be the square of a natural number.

In other words, the area of the floor will be a perfect square.

Checking the squares of a few natural numbers, we find:

Number	1	2	3	4	5	6	7	8	9
Square	1	4	9	16	25	36	49	64	81
Last digit of the square	1	4	9	6	5	6	9	4	1

Generalizing this, we find that all perfect squares have any one of the following digits in their ones places:

$1,4,5,6,9$

Now, of the given areas, the area 4337 sq ft has 7 in its ones place.

So, it cannot be a perfect square.

Hence, 4337 sq ft cannot be the area of the square floor.