Question

2025 plants are to be planted in a garden in such a way that each row contains as many as the number of rows find the number of rows and the number of plants in each row ​

Answer 1

Let the number of rows be x.

$\sf{\underline{Now:}}$

The number of plants in each row: x

$\sf{\underline{Therefore:}}$

Number of plants in x rows:

$\boxed{\sf{x \times x = {x}^{2}}}$

$\sf{\underline{That\:is:}}$

$\implies$ $\sf{ {x}^{2} = 2025}$

$\implies$ $\sf{x = \sqrt{2025} }$

$\sf{\underline{Prime\:factorisation\:of\:2025\:is:}}$

$\begin{array}{r | l} 3 & 2025 \\ \cline{2-2} 3 & 675 \\ \cline{2-2} 3 & 225 \\ \cline{2-2} 3 & 75 \\ \cline{2-2} 3 & 25 \\ \cline{2-2} 5 & 25 \\ \cline{2-2} 5 & 5 \\ \cline{2-2} & 1 \end{array}$

$\sf{\underline{That\:is:}}$

$\boxed{\sf{2025 = 3 \times 3 \times 3 \times 3 \times 5 \times 5}}$

Let $x = \sqrt{2025}$

$\sf{\underline{Now:}}$

$\implies$ $\sf{x = \sqrt{3 } \times \sqrt{3} \times \sqrt{3} \times \sqrt{3} \times \sqrt{5} \times \sqrt{5}}$

$\implies$ $\sf{x = 3 \times 3 \times 5}$

$\implies$ $\sf{x = 3 \times 15}$

$\implies$ $\boxed{\sf{x = 45}}$

$\sf{\underline{Therefore:}}$

The number of rows: 45
The number of plants in each row: 45

Answer 2

Total Plants=2025

2025 Planted in Garden Such that Total Rows =Plant in 1 row.

Let Total Row=x

Then we know

Total Row=Plant in 1 row.

Then In 1 row=x plants

Then In Total Row

Plant in 1 row×Total Row=Total Plant

x×x=2025

x²=2025

$x = \sqrt{2025} \\ \\ 2025 = 3 \times 3 \times 3 \times 3 \times 5 \times 5$

Make Pair of Two.

$x = \sqrt{ \underline{3 \times 3 \times 3 \times 3 \times 5 \times 5}} \\ \\ x = 3 \times 3 \times 5\\ \\ x = 45$

There Will be Total 45 Rows

And Total 45 Plants in Each Row.