Answer:
Let the number of rows be \[x\]. Then, number of plants in each row \[=x\]. \[\therefore \] Number of plants in \[x\] rows \[=x\times x={{x}^{2}}\]. But 2025 plants are to be planted in a garden. \[\therefore \] \[{{x}^{2}}=2025\,\,\Rightarrow \,\,x=\sqrt{2025}\] The prime factorisation of 2025 is
\[2025=\underline{3\times 3}\times \underline{3\times 3}\times \underline{5\times 5}\] \[\therefore \] \[x=\sqrt{2025}\,=\sqrt{\underline{3\times 3}\times \underline{3\times 3}\times \underline{5\times 5}}\] \[\Rightarrow \] \[x=3\times 3\times 5\,\,\Rightarrow \,\,x=45\] Hence, the number of rows is 45 and the number of plants in each row is 45. 3 2025 3 675 3 225 3 75 5 25 5
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