Introduction:

To find the least number that must be added to 280567 to make it a perfect square, we first need to understand what a perfect square is and how we can find it.

What is a perfect square?

A perfect square is a number that can be expressed as the product of an integer multiplied by itself. For example, 4, 9, 16, and 25 are perfect squares because they can be expressed as 2^2, 3^2, 4^2, and 5^2 respectively.

Finding the perfect square:

To find the perfect square that is closest to 280567, we can start by taking the square root of 280567 and rounding it up to the nearest whole number. Let's calculate it step by step:

1. Take the square root of 280567:
- √280567 ≈ 529.604

2. Round up the square root to the nearest whole number:
- Rounded up to the nearest whole number, the square root is 530.

3. Calculate the square of the rounded-up number:
- 530^2 = 280900

Finding the difference:

Now that we have the perfect square closest to 280567, we can find the difference between the perfect square and 280567 to determine the least number that must be added to make it a perfect square.

1. Calculate the difference:
- Difference = Perfect square - 280567
- Difference = 280900 - 280567 = 333

So, the least number that must be added to 280567 to make it a perfect square is 333.

Conclusion:

In conclusion, the least number that must be added to 280567 to make it a perfect square is 333. By following the steps of finding the perfect square and calculating the difference, we can determine the number needed to achieve the desired result.