Introduction:

To find the least number that must be added to 424873 to make it a perfect square, we need to first determine the closest perfect square to 424873 and then calculate the difference between the two values.

Identifying the closest perfect square:

To find the closest perfect square to 424873, we can start by calculating the square root of 424873.

√424873 ≈ 651.4

The closest perfect square to 424873 will be the square of the nearest whole number, which is 651.

651^2 = 424801

Calculating the difference:

Now, we need to calculate the difference between the closest perfect square and 424873.

424873 - 424801 = 72

So, the difference between 424873 and the closest perfect square is 72.

Finding the least number to be added:

To make 424873 a perfect square, we need to add a number which, when added to 424873, will result in a perfect square.

Let's assume the number to be added is x.

424873 + x = 424873 + 72

The resulting sum should be a perfect square. To find the least value of x, we need to determine the next perfect square after 424873 + 72.

The next perfect square after 424873 + 72 is:

425000 + 72 = 425072

Therefore, the least number that must be added to 424873 to make it a perfect square is 72.

Summary:

To summarize, we found that the closest perfect square to 424873 is 424801. The difference between 424873 and the closest perfect square is 72. To make 424873 a perfect square, we need to add 72 to it. Thus, the least number that must be added to 424873 to make it a perfect square is indeed 72.