Question

# $2025$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.

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Solution

## Given that,The number of plants in a garden are $2025$.Let's assume the number of rows in a garden be,$R$So, each row has a number of plants $R$Therefore, total number of plants $=$ $R$ $×$ $R$That indicates $R$ $×$ $R$ $=$ $2025$ The prime factorization of $2025$ is shown below,$R$ $×$ $R$ $=$ $2025$ ${R}^{2}$ $=$ $\left(3×3\right)×\left(3×3\right)×\left(5×5\right)$ ${R}^{2}$ $=$$\left(3×3×5\right)×\left(3×3×5\right)$ ${R}^{2}$ $=$ $45×45$ $R$ $=$ $\sqrt{\left(45×45\right)}$ $R$ $=$ $45$Therefore, the number of rows, $R$ $=$ $45$The number of plants in each row, $R$ $=$ $45$ .Hence, the number of rows is $45$ and the number of plants in each row is $45$.

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