The members of the set S={x|x is a square of an integer and x<100} is

The set \( S = \{ x \mid x \text{ is a square of an integer and } x < 100 \} \) contains all the perfect squares that are less than 100. 

To find the members of this set, we calculate the squares of integers, starting from 1, until the square exceeds 100.

\[
1^2 = 1,\ 2^2 = 4,\ 3^2 = 9,\ 4^2 = 16,\ 5^2 = 25,\ 6^2 = 36,\ 7^2 = 49,\ 8^2 = 64,\ 9^2 = 81
\]

Since \( 10^2 = 100 \), which is not less than 100, we stop at 9.

Thus, the set \( S \) is:
\[
S = \{1, 4, 9, 16, 25, 36, 49, 64, 81\}
\]

Do you have any questions, or would you like more details?

Here are 5 related questions:
1. What are the perfect squares less than 200?
2. How can you represent this set \( S \) using set-builder notation?
3. How many perfect squares are there between 100 and 500?
4. What is the largest perfect square less than 1000?
5. How can you check if a number is a perfect square?

**Tip:** A perfect square is always the result of an integer multiplied by itself.

Explore the set of perfect squares less than 100. Learn how to find the squares of integers, such as 1^2, 2^2, 3^2, up to 9^2, resulting in the set {1, 4, 9, 16, 25, 36, 49, 64, 81}. This problem covers key concepts in number theory and set theory, suitable for students in Grades 6-8.

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