### Instruction: The product of two consecutive page numbers is $18{,}360.$ What is the sum of the two page numbers?### Response: I need to find two consecutive page numbers that multiply to $18{,}360.$
I could try to factor $18{,}360$ and look for two factors that are one apart, but that might take a long time.
Instead, I'll use a shortcut: I know that the square root of $18{,}360$ is about $135.5,$ since $135^2 = 18{,}225$ and $136^2 = 18{,}496.$
That means the two page numbers must be close to $135.5,$ one below and one above.
I'll try $135$ and $136$ and see if they work.
$135 \times 136 = 18{,}360,$ so I found the correct page numbers.
The sum of the two page numbers is $135 + 136 = 271.$