Express the following square number as the sun of two consecutive natural number. 441

To express the square number \( 441 \) as the sum of two consecutive natural numbers, follow these steps:

1. **Identify the square root of 441:**
   \[
   \sqrt{441} = 21
   \]
   So, \( 441 = 21^2 \).

2. **Use the formula:**
   For any square number \( n^2 \), the two consecutive numbers can be calculated as:
   \[
   x = \frac{n^2 - 1}{2}
   \]
   \[
   x + 1 = \frac{n^2 + 1}{2}
   \]

   Here, \( n = 21 \), so:
   \[
   x = \frac{21^2 - 1}{2} = \frac{441 - 1}{2} = \frac{440}{2} = 220
   \]
   \[
   x + 1 = \frac{21^2 + 1}{2} = \frac{441 + 1}{2} = \frac{442}{2} = 221
   \]

3. **Conclusion:**
   The two consecutive natural numbers are \( 220 \) and \( 221 \).

Thus, \( 441 = 220 + 221 \).

Would you like further details or have any questions?

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### Related Questions:
1. How can you verify that 441 is a perfect square?
2. What is the significance of consecutive natural numbers in the context of number theory?
3. Can 441 be expressed as the sum of three or more consecutive natural numbers?
4. How do we find the sum of the first \( n \) natural numbers, and how does it relate to square numbers?
5. Is there a method to express a square number as the sum of four consecutive natural numbers?

### Tip:
When dealing with consecutive natural numbers, the sum of the first \( n \) natural numbers can also be related to triangular numbers, which offers another interesting perspective in number theory.

Learn how to express the square number 441 as the sum of two consecutive natural numbers using a step-by-step approach. This problem involves understanding square numbers, consecutive natural numbers, and their relationship in number theory. Suitable for Grades 6-8 students.

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