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?

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.