Understanding the Problem
To determine how many numbers lie between the squares of 12 and 13, we first need to calculate these squares.
Squares of 12 and 13
- The square of 12 is calculated as:
- 12 * 12 = 144
- The square of 13 is calculated as:
- 13 * 13 = 169
Identifying the Range
Now, we have identified the squares:
- Square of 12: 144
- Square of 13: 169
The task is to find all the numbers that lie between these two squares.
Finding the Numbers
To find the numbers between 144 and 169, we consider:
- The smallest number greater than 144 is 145.
- The largest number less than 169 is 168.
Counting the Numbers
To count the numbers between 145 and 168:
- Start from 145 and go up to 168:
- The sequence of numbers is: 145, 146, 147, ..., 168
To find the total count:
- The total numbers can be counted using the formula:
- Total = Last number - First number + 1
- Total = 168 - 145 + 1 = 24
Conclusion
Thus, there are a total of 24 numbers between the squares of 12 and 13.