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9.There 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 the number of columns. How many children would be left out in this arrangement?
Answer :

Let the number of children in a row and column each be x.
Total number of students = \(x \times x = x^2\)

\(x^2 = 500\)

\(\Rightarrow x = \sqrt{500}\)

\(\qquad \begin{array}{c|lcr} &22\\ \hline 2 &\;\; \;\bar{5}\bar{00}\\ &\;-4\\ \hline 42 &\;\;\; \;\;100\\ &\;\;\;\;\;84\\ \hline &\;\;\;\;\;16\\ \hline \end{array} \)

We got the remainder as 16.

So the new number is = 500 – 16 = 484

and, \(\sqrt{484} = 22\)

Thus, 16 students will be left out in this arrangement.