Evaluate:
`sqrt(6241)`

Answer

To evaluate \( \sqrt{6241} \) using the long division method, follow these steps:

### Step 1: Pair the digits
Starting from the right, pair the digits of the number. For 6241, we can pair them as (62)(41).

### Step 2: Find the largest square
Now, we need to find the largest square number less than or equal to the first pair (62). The squares of integers are:
- \( 7^2 = 49 \)
- \( 8^2 = 64 \)

Since \( 64 \) is greater than \( 62 \), we take \( 7^2 = 49 \).

### Step 3: Subtract and bring down the next pair
Subtract \( 49 \) from \( 62 \):
\[ 62 - 49 = 13 \]
Now, bring down the next pair (41) next to 13 to get 1341.

### Step 4: Double the quotient
Double the quotient we found (which is 7):
\[ 2 \times 7 = 14 \]

### Step 5: Find the next digit
Now, we need to find a digit \( x \) such that:
\[ (140 + x) \times x \leq 1341 \]
Testing \( x = 9 \):
\[ (140 + 9) \times 9 = 149 \times 9 = 1341 \]

This works perfectly, so we have found the next digit.

### Step 6: Write down the result
The quotient we have found is \( 79 \). Therefore, we conclude:
\[ \sqrt{6241} = 79 \]

### Final Answer
Thus, the square root of \( 6241 \) is \( 79 \).

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