`sqrt(8281)=?`

Options

A. 89
B. 97
C. 93
D. 91

Explanation

To find the square root of 8281 using the long division method, we can follow these steps:

### Step 1: Pair the digits
Start from the right and pair the digits of the number. For 8281, we can pair it as (82)(81).

### Step 2: Find the largest square
Look for the largest square number less than or equal to the first pair (82). The largest square is 9^2 = 81.

### Step 3: Write down the quotient
Write down 9 as the first digit of the quotient.

### Step 4: Subtract and bring down the next pair
Subtract 81 from 82, which gives us 1. Now, bring down the next pair (81) next to the remainder (1), making it 181.

### Step 5: Double the quotient
Double the current quotient (which is 9) to get 18.

### Step 6: Find the next digit
Now, we need to find a digit (let's call it x) such that (180 + x) * x is less than or equal to 181. Testing x = 1:
- (180 + 1) * 1 = 181, which is equal to 181.

### Step 7: Write down the next digit
So, we write down 1 next to the quotient, making it 91.

### Step 8: Subtract again
Subtract 181 from 181, which gives us 0.

### Step 9: Conclusion
Since there are no more digits to bring down and the remainder is 0, we conclude that the square root of 8281 is 91.

Thus, we have:
\[ \sqrt{8281} = 91 \]