Question

These are \(500\) children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement?

Answer 1

It is given that there are \(500\) children in the school. They have to stand for a P.T. drill such that the number of rows is equal to the number of columns.
The number of children who will be left out in this arrangement has to be calculated. That is, the number which should be subtracted from \(500\) to make it a perfect square has to be calculated.
The square root of \(500\) can be calculated by long division method as follows.

	22
2	\(\bar 5\) \(\bar0\bar 0\) -4
42	100 84
	16

The remainder is \(16.\)
It shows that the square of \(22\) is less than \(500\) by \(16\). 
Therefore, if we subtract \(16\) from \(500\), we will obtain a perfect square.
Required perfect square = \(500 - 16 = 484\)

Thus, the number of children who will be left out is \(16\).