A teacher has to arrange 1000 students in several rows so that each row contains as many students as the total number of rows. Do you think the teacher will be able to arrange all of these students in the way mentioned in the problem? How many students will be left out after the arrangement is done?

No, the teacher won't be able to make the arrangement

If he tries making the arrangement, 39 students would be left out out of the 1000

Step-by-step explanation:

This will not be possible because, the number of students to arrange is 1000 and it is not a perfect square. So there won't be a possibility of having the same number of students per row as the number of rows.

If 1000 was a perfect square, it would have been possible

Now, to calculate the number of students that would be left if the teacher proceeded with the arrangement, what we need is that perfect square which is closest to 1000 but less than it.

Since 30 * 30 = 900

The next number to try is 31 * 31 = 961

32 squared won't work as it is 1024 and the value is greater than 1000

Now, the number of students left would be 1000-961 = 39