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

To express a square number as the sum of two consecutive natural numbers, follow these steps:

1. Let the square number be \( n^2 \).
2. We need to express \( n^2 \) as the sum of two consecutive numbers. Let's denote these consecutive numbers as \( x \) and \( x+1 \).
3. The sum of these two consecutive numbers is \( x + (x + 1) = 2x + 1 \).

We want \( n^2 = 2x + 1 \). 

4. To solve for \( x \), rearrange the equation:

\[
2x = n^2 - 1
\]
\[
x = \frac{n^2 - 1}{2}
\]

So, the two consecutive natural numbers are:

\[
x = \frac{n^2 - 1}{2}
\]
\[
x+1 = \frac{n^2 + 1}{2}
\]

### Example:

Let's express \( 25 \) as the sum of two consecutive natural numbers.

1. Here, \( n = 5 \), so \( n^2 = 25 \).
2. Calculate \( x \):

\[
x = \frac{25 - 1}{2} = \frac{24}{2} = 12
\]

3. The two consecutive numbers are \( 12 \) and \( 13 \).

Thus, \( 25 = 12 + 13 \).

Would you like further details or have any questions?

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### Related Questions:
1. How can any square number be expressed as the difference of two squares?
2. What is the general formula for expressing any perfect square as the sum of consecutive odd numbers?
3. Can a square number be expressed as the sum of three consecutive natural numbers?
4. How do you prove that the sum of any two consecutive natural numbers is always odd?
5. What is the significance of consecutive sums in number theory?

### Tip:
For any square number \( n^2 \), the sum of two consecutive natural numbers can be found directly using the formula \( n^2 = \frac{(n^2 - 1)}{2} + \frac{(n^2 + 1)}{2} \).

Learn how to express a square number as the sum of two consecutive natural numbers with a detailed step-by-step solution. This problem involves basic algebraic concepts and is suitable for students in Grades 6-8.

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