Determine whether or not the following sentence is a logical statement.

"1024 is the smallest 4-digit number that is a perfect square."

Yes, the sentence **"1024 is the smallest 4-digit number that is a perfect square."** is a logical statement. 

This sentence makes a definitive claim about a mathematical property, specifically that 1024 is the smallest 4-digit number that is also a perfect square. 

To analyze whether this claim is true:
- A 4-digit number is any number between 1000 and 9999.
- 1024 is indeed a 4-digit number.
- To check if it is a perfect square, we find its square root:  
  \[
  \sqrt{1024} = 32
  \]
  So, 1024 is a perfect square (32² = 1024).

Next, we check if it is the smallest 4-digit perfect square:
- The smallest 4-digit number is 1000. 
- The square root of 1000 is approximately 31.62, which is not an integer, so 1000 is not a perfect square.
- The square root of the next integer 32 (which is 1024) is indeed a perfect square.

Hence, the statement is both logical and true.

Would you like more details on this, or do you have any other questions?

Here are some related questions:
1. What is a perfect square, and how is it defined?
2. How can we find if a number is a perfect square?
3. What are the properties of perfect squares?
4. Can there be negative perfect squares?
5. How can we determine if a statement is logical?

**Tip:** When analyzing mathematical statements, it's important to break down each component and verify it step by step.

Explore the logic behind the statement '1024 is the smallest 4-digit number that is a perfect square.' This problem delves into number theory concepts such as perfect squares and square roots, providing a detailed step-by-step analysis. Suitable for students in Grades 6-8.

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