how many numbers are there between 10² and 12²

We are asked to find how many numbers lie between \(10^2\) and \(12^2\).

1. First, calculate \(10^2\) and \(12^2\):
   \[
   10^2 = 100 \quad \text{and} \quad 12^2 = 144
   \]
   
2. Now, we need to find the numbers strictly between 100 and 144. This means we exclude 100 and 144 themselves.

So, we are looking for numbers from 101 to 143.

3. The count of numbers from 101 to 143 can be found using the formula for the number of integers between two numbers \(a\) and \(b\):
   \[
   \text{Count} = b - a + 1
   \]
   Here, \(a = 101\) and \(b = 143\):
   \[
   \text{Count} = 143 - 101 + 1 = 43
   \]

Therefore, there are 43 numbers between \(10^2\) and \(12^2\).

Would you like more details or have any questions? Here are some related questions you might find interesting:
1. How many numbers lie between \(15^2\) and \(18^2\)?
2. What is the sum of all numbers between \(10^2\) and \(12^2\)?
3. How many perfect squares are there between \(10^2\) and \(12^2\)?
4. How can we generalize the formula to find numbers between any two squares \(a^2\) and \(b^2\)?
5. Can you list all prime numbers between \(10^2\) and \(12^2\)?

**Tip:** When calculating how many numbers are between two values, always remember to subtract the lower number from the higher one and adjust for inclusivity or exclusivity.

Discover how to calculate the number of integers between 10² and 12². This problem explores basic arithmetic concepts such as number range, exponents, and the formula to count integers between two values. Suitable for Grades 6-8 students.

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