Math Problem Statement

Determine whether or not the following sentence is a logical statement: '1024 is the smallest 4-digit number that is a perfect square.'

Solution

The sentence presented is: "1024 is the smallest 4-digit number that is a perfect square."

This is a statement, as it is a declarative sentence that can be evaluated as true or false.

To verify:

  • The smallest 4-digit number is 1000.
  • The smallest perfect square in the range of 4-digit numbers is 322=102432^2 = 1024.
  • Hence, the statement is true.

Do you want further details or explanations? Here are some related questions to explore:

  1. What are the next largest perfect squares after 1024?
  2. How can we mathematically confirm if a number is a perfect square?
  3. What is the significance of logical statements in mathematics?
  4. Can you provide more examples of statements versus non-statements?
  5. How do we determine the smallest n-digit number that satisfies a given property?

Tip: Always verify logical statements by breaking them into components and checking each part's truth value.

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Math Problem Analysis

Mathematical Concepts

Number theory
Perfect squares
Logical statements

Formulas

n^2 where n is an integer

Theorems

Definition of perfect squares

Suitable Grade Level

Grades 6-8