Question

In a school Auditorium ,the number of chairs in each row is same as the number of rows of chair .There are 7033 students in a school if we know that less than 31 chairs were empty, how many chairs were empty after all students Sat down.

Answer 1

The number of chairs in each row = The number of rows
Consider no. of rows as height and number of chairs in each row as width, so

This means that it is like a square.
So, Total students = 7033
If we find the sq root of 7033

we get a number = 83.8... (something in decimals)
As, we know that total no. of chairs > 7033 , because there were empty chairs. 
So, we find the next nearest natural number to 83.8, i.e. 84
So, 84² = 7056
We have total 7056 chairs
Empty chairs = 7056 - 7033 = 23 ( which should be less than 31)
Therefore, no. of empty chairs after all students sat, were 23