What will be the square root of 7921 ?

Options

A. 89
B. 87
C. 37
D. 47

Answer

To find the square root of 7921 using the long division method, follow these steps:

### Step-by-Step Solution:

1. **Pair the Digits**: Start from the right and pair the digits of the number 7921. We have:
- Pair 1: 21
- Pair 2: 79

2. **Find the Largest Square**: Look for the largest square number less than or equal to the first pair (79). The largest square is 64 (which is 8²).
- Write 8 above the line and subtract 64 from 79:
\[ 79 - 64 = 15 \]

3. **Bring Down the Next Pair**: Bring down the next pair (21) next to the remainder (15), making it 1521.

4. **Double the Quotient**: Double the number above the line (which is 8). So, 8 × 2 = 16. Write this down:
- Now we have: 16_

5. **Find the Next Digit**: We need to find a digit (let's call it x) such that:
\[ (16x) \times x \leq 1521 \]
Testing x = 9:
\[ (16 \times 9) \times 9 = 144 \times 9 = 1296 \quad (\text{which is less than } 1521) \]
Testing x = 10:
\[ (16 \times 10) \times 10 = 160 \times 10 = 1600 \quad (\text{which is greater than } 1521) \]
So, we use x = 9.

6. **Subtract**: Now, we subtract 1296 from 1521:
\[ 1521 - 1296 = 225 \]

7. **Final Result**: Since we have no more pairs to bring down, we can conclude that:
- The number above the line is 89, which means:
\[ \sqrt{7921} = 89 \]

### Final Answer:
The square root of 7921 is **89**.