https://file.aiquickdraw.com/mathbot/file/17282042810026bzmavvx.jpg

The pattern shown in the image involves a relationship between the numbers in the top and bottom rows. Let's analyze it:

- The top number is a perfect square: \(16 = 4^2\), \(36 = 6^2\), and \(121 = 11^2\).
- The bottom two numbers are also perfect squares:
  - For \(16\): The bottom numbers are \(4 = 2^2\) and \(9 = 3^2\).
  - For \(36\): The bottom numbers are \(16 = 4^2\) and \(25 = 5^2\).
  - For \(121\): The bottom numbers are \(81 = 9^2\) and the missing number, which should follow the same pattern.

From the sequence \(2^2, 3^2, 4^2, 5^2, 9^2\), the next perfect square would logically be \(10^2 = 100\).

Thus, the missing number is **100**.

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Would you like any additional details or explanations? Here are 5 questions that could extend this:

1. What other types of number patterns could exist in problems like this?
2. How can perfect squares be used in geometric progressions?
3. What are the properties of square numbers and how can they be applied in puzzles?
4. Can other powers (like cubes) be applied in similar patterns?
5. How can number pattern problems be approached systematically?

**Tip:** When solving number patterns, identifying any recurring operations (like squares, cubes, or arithmetic progressions) can quickly guide you to the solution.

Select the missing number from the given alternatives.

Explore how to find the missing number in a pattern of perfect squares. This problem involves identifying the relationship between numbers such as 16, 36, and 121 and using perfect square sequences to solve it. Suitable for students in Grades 6-8.

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