Number System Practice Test 1

Let the four consecutive odd numbers be (2x – 3), (2x – 1), (2x + 1) and (2x + 3)
∴ Their product = (2x - 1) (2x + 1) (2x - 3) (2x + 3)
$=\left(4{\mathit{x}}^2-1\right)\left(4{\mathit{x}}^2-9\right)$
$=16{\mathit{x}}^4-40{\mathit{x}}^2+9$
$={\left(4{\mathit{x}}^2-5\right)}^2-16$
Hence, on adding 16, the result will be a perfect square.