One number is equal to the square of another. find the numbers if both are positive and their sum is 18921892.

If n is the number, the sum is
.. n^2 +n = 1892
The solution to this quadratic is
.. n = 43

Your numbers are 1849 and 43.


The product n^2 +n can be written as n(n+1). Since n is fairly large,
.. n + 1/2 ≈ √(n*(n +1))
.. √1892 ≈ 43.497 ≈ 43 1/2
so n = 43.
There are more formal ways to get this result exactly, but it is often convenient to use a square root like this to get you close to the number of interest.