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7.The students of class VIII of a school donated ₹ 2401 in all, for the Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.
Answer :

Let x be the number of students in the class. Therefore, total money donated by students:\(x \times x=₹ x^2\)
Here we have, \(x^2 =2401\)

\(\Rightarrow x=\sqrt{2401}\)

\(\qquad \begin{array}{c|lcr} 7 & 2401\\ \hline 7 & 343\\ \hline 7 & 49\\ \hline 7 & 7\\ \hline & 1\\ \end{array} \)

\(\Rightarrow x=\sqrt{7 \times 7 \times 7 \times 7}\)

\(\Rightarrow x=7 \times 7 \)

\(\Rightarrow x=49\)

Hence, the number of the students in the class is 49.