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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.