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.