A gardener plants 2025 plants in a garden. She arranges them in rows such that the number of plants in each row is equal to the number of rows. How many plants are in each row?

Let the number of rows be $x$.
According to the problem, each row contains as many plants as the number of rows. So, the number of plants in each row is also $x$.
The total number of plants is the product of the number of rows and the number of plants in each row.
Total plants = Number of rows $\times$ Number of plants in each row
Total plants = $x \times x = x^2$.

We are given that the total number of plants is 2025.
So, we have the equation:

$$x^2 = 2025$$

First, find the prime factors of 2025:

$$2025 = 5 \times 405$$ $$405 = 5 \times 81$$ $$81 = 3 \times 27$$ $$27 = 3 \times 9$$ $$9 = 3 \times 3$$

So, the prime factorization of 2025 is $3 \times 3 \times 3 \times 3 \times 5 \times 5$.
We can write this as $3^4 \times 5^2$.

$$x = \sqrt{3^4 \times 5^2}$$ $$x = \sqrt{(3^2)^2 \times 5^2}$$ $$x = 3^2 \times 5^1$$ $$x = 9 \times 5$$ $$x = 45$$

The number of rows is 45, and the number of plants in each row is 45.

The number of rows and the number of plants in each row is 45.