What is the smallest square number, which is the sum of two other square numbers?

To find the smallest square number that is the sum of two other square numbers, we can use the concept of Pythagorean triples. A Pythagorean triple consists of three positive integers $a$, $b$, and $c$ such that $a^2 + b^2 = c^2$. Here, $c^2$ is the square number we are looking for.

Let's go through the steps to find the smallest such $c^2$:

1. Identify the smallest Pythagorean triple: The smallest Pythagorean triple is (3, 4, 5). This means: $3^2 + 4^2 = 5^2$

2. Calculate the squares: $3^2 = 9$ $4^2 = 16$ $5^2 = 25$

3. Verify the sum: $9 + 16 = 25$

4. Conclusion: The smallest square number that is the sum of two other square numbers is $25$.

So, the smallest square number which is the sum of two other square numbers is $25$.