### Instruction: How many perfect squares have a value between 10 and 1000?### Response: A perfect square is a number that can be written as the square of an integer.
For example, 4 is a perfect square because it is 2^2, and 9 is a perfect square because it is 3^2.
To find the perfect squares between 10 and 1000, I need to identify the smallest and largest integers whose squares are in this range.
The smallest integer whose square is greater than 10 is 4, because 4^2 = 16 and 3^2 = 9.
The largest integer whose square is less than 1000 is 31, because 31^2 = 961 and 32^2 = 1024.
Therefore, the integers whose squares are between 10 and 1000 are 4, 5, 6, ..., 30, and 31.