Evaluate:
`sqrt (11449)`

Answer

To evaluate \( \sqrt{11449} \) using the long division method, follow these steps:

### Step 1: Pair the digits
Start from the right and pair the digits of the number 11449. We can pair them as follows:
- Pair 49 (the last two digits)
- Pair 14 (the next two digits)
- The single digit left is 1.

So we have the pairs: \( 1 | 14 | 49 \).

### Step 2: Find the largest square
Now, we will find the largest square that is less than or equal to the first pair (1). The largest square is \( 1^2 = 1 \).

### Step 3: Subtract and bring down the next pair
Subtract \( 1 \) from \( 1 \):
\[ 1 - 1 = 0 \]
Now, bring down the next pair (14) to get 014.

### Step 4: Double the divisor
Double the number we found (which is 1) to get 2. We will now find a digit \( x \) such that \( (20 + x) \times x \) is less than or equal to 14.

### Step 5: Find the suitable digit
Testing \( x = 0 \):
\[ (20 + 0) \times 0 = 0 \quad \text{(valid)} \]
Testing \( x = 1 \):
\[ (20 + 1) \times 1 = 21 \quad \text{(not valid)} \]
So, we take \( x = 0 \).

### Step 6: Subtract and bring down the next pair
Now, we have:
\[ 0 \text{ (from the previous step)} + 14 = 14 \]
Subtract \( 0 \) from \( 14 \):
\[ 14 - 0 = 14 \]
Now bring down the next pair (49) to get 1449.

### Step 7: Double the divisor again
Double the current quotient (which is 10) to get 20. Now we need to find a digit \( y \) such that \( (200 + y) \times y \) is less than or equal to 1449.

### Step 8: Find the suitable digit
Testing \( y = 7 \):
\[ (200 + 7) \times 7 = 207 \times 7 = 1449 \quad \text{(valid)} \]
So, we take \( y = 7 \).

### Step 9: Final result
Now, we have found that the square root of \( 11449 \) is \( 107 \) because:
\[ 10 + 7 = 107 \]

Thus, \( \sqrt{11449} = 107 \).

### Final Answer:
\[ \sqrt{11449} = 107 \]