Question

a ballroom had a square dance floor. The area of the floor is 400 square feet. If the length of each side of the square increased by one foot, would its area be a rational number?

Answer 1

Yes

Explanation:

The area of a square is equal to the length squared.

So, the length of one side of the original floor is √400 which equals 20.

If you increase the length by 1, the area of the dance floor is 21 squared.

21 * 21 is certainly a rational number.

Answer 2

Explanation:

I think so, yes.

The area of a square is A = s*s where s is the length of the side

s^2 = 400

sqrt(s^2) = sqrt(400)

s = 20

If you increase each dimension by one foot you get 21 * 21 for the area of the new ballroom.

The result is rational. That's because the square root was rational when you found 20.

Area = 21 * 21 = 441 which is rational.