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8.2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.
Answer :

Let the number of rows be x and x be the number of plants in each row.
∴we have total number of plants=\(x^2\) = \(\sqrt{2025}\)

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

\(\qquad \begin{array}{c|lcr} 3 & 2025\\ \hline 3 & 675\\ \hline 3 & 225\\ \hline 3 & 75\\ \hline 5 & 25\\ \hline 5 & 5\\ \hline & 1\\ \end{array} \)

\(\Rightarrow \sqrt { 3\times 3\times 3\times 3\times 5\times 5 }\)

\(\Rightarrow \sqrt { { 3 }^{ 2 }\times { 3 }^{ 2 }\times { 5 }^{ 2 } }\)

\(\Rightarrow 3 \times 3 \times 5\)

\(\Rightarrow 45\)
Hence, the number of rows is 45 and the number of plants in each row is also 45