question_answer 1)

                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 \[x\]. 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

3	2025
3	675
3	225
3	75
5	25
	5

  \[2025=\underline{3\times 3}\times \underline{3\times 3}\times \underline{5\times 5}\] \[\therefore \]  \[x=\sqrt{2025}\,=\sqrt{\underline{3\times 3}\times \underline{3\times 3}\times \underline{5\times 5}}\] \[\Rightarrow \]               \[x=3\times 3\times 5\,\,\Rightarrow \,\,x=45\] Hence, the number of rows is 45 and the number of plants in each row is 45.