Number of non-square numbers between 112 and 122:

To determine the number of non-square numbers between 112 and 122, we need to find the square numbers within this range and subtract them from the total count.

1. Identifying the square numbers:
- Start by finding the square root of the lower limit (112) and rounding it up to the nearest whole number. The square root of 112 is approximately 10.58, so we round it up to 11.
- Next, find the square root of the upper limit (122) and round it down to the nearest whole number. The square root of 122 is approximately 11.05, so we round it down to 11.
- The numbers between the rounded square roots (11) are the square numbers within the range. In this case, 11 * 11 = 121 is the only square number between 112 and 122.

2. Finding the count of non-square numbers:
- To determine the count of non-square numbers, subtract the count of square numbers (1) from the total count of numbers in the range.
- The total count of numbers between 112 and 122 is 122 - 112 + 1 = 11.
- Subtracting the count of square numbers (1) from the total count gives us 11 - 1 = 10.

Therefore, there are 10 non-square numbers between 112 and 122.