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.

Options

A. `44`
B. `46`
C. `45`
D. `40`

Explanation

To solve the problem of planting 2025 plants in a garden such that the number of rows is equal to the number of plants in each row, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables**:
Let the number of rows be \( x \). Since each row contains as many plants as the number of rows, the number of plants in each row is also \( x \).

2. **Set Up the Equation**:
The total number of plants can be expressed as:
\[ \text{Total plants} = \text{Number of rows} \times \text{Number of plants in each row} = x \times x = x^2 \]
According to the problem, the total number of plants is 2025. Therefore, we can write the equation:
\[ x^2 = 2025 \]

3. **Solve for \( x \)**:
To find \( x \), we need to take the square root of both sides of the equation:
\[ x = \sqrt{2025} \]

4. **Calculate the Square Root**:
We will calculate \( \sqrt{2025} \) using the long division method or by recognizing perfect squares:
- Pair the digits of 2025 from right to left: (20)(25).
- Find the largest perfect square less than or equal to 20, which is \( 4 \) (since \( 4^2 = 16 \)).
- Subtract \( 16 \) from \( 20 \) to get \( 4 \) and bring down \( 25 \) to get \( 425 \).
- Double the quotient (which is 4) to get \( 8 \) and find a digit \( d \) such that \( (80 + d) \times d \leq 425 \). Testing \( d = 5 \):
\[ 85 \times 5 = 425 \]
- Subtract to get \( 0 \), confirming that \( 2025 \) is a perfect square.

5. **Conclusion**:
Thus, \( x = 45 \). Therefore, the number of rows is \( 45 \) and the number of plants in each row is also \( 45 \).

### Final Answer:
- Number of rows = 45
- Number of plants in each row = 45