Gopal wants to plant 99225 shrubs and arranges them in such a way that there are as many rows as there are shrubs in a row. Find the number of shrubs in a row.

Options

A. 315
B. 165
C. 625
D. 225

Answer

To solve the problem of how many shrubs Gopal can plant in each row, we need to find the square root of the total number of shrubs, which is 99225. This is because the number of rows is equal to the number of shrubs in each row.

### Step-by-Step Solution:

1. **Identify the total number of shrubs**:
\[ \text{Total shrubs} = 99225 \]

2. **Set up the equation**:
Let \( x \) be the number of shrubs in each row. Since the number of rows is also \( x \), we have:
\[ x \times x = 99225 \quad \text{or} \quad x^2 = 99225 \]

3. **Calculate the square root**:
To find \( x \), we need to calculate:
\[ x = \sqrt{99225} \]

4. **Finding the square root**:
To find the square root of 99225, we can use the method of prime factorization or long division. Here, we will use the long division method:
- Pair the digits from right to left: (99)(22)(25)
- Find the largest number whose square is less than or equal to 99. That number is 9 (since \( 9^2 = 81 \)).
- Subtract \( 81 \) from \( 99 \) to get \( 18 \).
- Bring down the next pair (22) to make it 1822.
- Double the divisor (9) to get 18 and find a digit \( d \) such that \( (180 + d) \times d \) is less than or equal to 1822. The digit \( d \) is 1 (since \( 181 \times 1 = 181 \)).
- Subtract to get \( 1822 - 181 = 1641 \).
- Bring down the next pair (25) to make it 164125.
- Double the current result (91) to get 182 and find a digit \( d \) such that \( (1820 + d) \times d \) is less than or equal to 164125. The digit \( d \) is 5 (since \( 1825 \times 5 = 9125 \)).
- Subtract to get \( 164125 - 9125 = 0 \).

5. **Final result**:
Thus, we find that:
\[ x = 315 \]

Therefore, the number of shrubs in each row is **315**.