To find the sum of all perfect squares between 10 and 60, we first need to identify the perfect squares within that range.

A perfect square is a number that is the square of an integer.

1. The smallest integer whose square is greater than 10 is $4$, since $4^2 = 16$.
2. The largest integer whose square is less than 60 is $7$, since $7^2 = 49$.

Now, the perfect squares between 10 and 60 are: $16 = 4^2, \quad 25 = 5^2, \quad 36 = 6^2, \quad 49 = 7^2$

Next, we sum these values: $16 + 25 + 36 + 49 = 126$

So, the sum of all perfect squares between 10 and 60 is 126.

Would you like any further details or have questions?

Here are 5 related questions you might explore:

1. What are the perfect squares between 100 and 500?
2. How many perfect squares are there between 1 and 100?
3. How do you determine if a number is a perfect square?
4. What is the sum of the squares of the first 10 integers?
5. Can you find perfect cubes between 10 and 100?

Tip: Perfect squares grow quadratically, so the gaps between consecutive squares increase as numbers get larger.