Evaluate:
`sqrt(7056)`

Answer

To evaluate \( \sqrt{7056} \), we will follow a step-by-step approach:

### Step 1: Pair the digits
We start by pairing the digits of the number from right to left. For 7056, we can pair them as follows:
- The pairs are: 70 and 56.

### Step 2: Find the largest square less than or equal to the first pair
Now, we will look at the first pair, which is 70. We need to find the largest integer whose square is less than or equal to 70.
- The squares of integers are:
- \( 7^2 = 49 \)
- \( 8^2 = 64 \)
- \( 9^2 = 81 \) (this is too large)

The largest square less than or equal to 70 is \( 8^2 = 64 \).

### Step 3: Subtract the square from the first pair
Now we subtract 64 from 70:
\[ 70 - 64 = 6 \]

### Step 4: Bring down the next pair
Next, we bring down the next pair, which is 56, next to the remainder:
\[ 6 \quad 56 \quad \Rightarrow \quad 656 \]

### Step 5: Double the number found in Step 2
We take the number we found in Step 2 (which is 8) and double it:
\[ 2 \times 8 = 16 \]

### Step 6: Find the next digit
Now we need to find a digit \( x \) such that \( (160 + x) \times x \) is less than or equal to 656. We will test digits from 1 to 9:
- For \( x = 4 \):
\[ (160 + 4) \times 4 = 164 \times 4 = 656 \]
This works perfectly.

### Step 7: Combine the results
Now we combine the digits we found:
- The first digit was 8 and the second digit is 4, so:
\[ \sqrt{7056} = 84 \]

### Final Result
Thus, the value of \( \sqrt{7056} \) is \( 84 \).

---