What will come in place of question mark (?) .
`11 xx 11 + (?)^2 + 13 xx 13 = 1068`

Options

A. 8
B. 6
C. 5
D. None of these

Answer

To solve the equation \( 11 \times 11 + (?)^2 + 13 \times 13 = 1068 \), we can follow these steps:

### Step 1: Calculate \( 11 \times 11 \) and \( 13 \times 13 \)
First, we calculate the squares:
- \( 11 \times 11 = 121 \)
- \( 13 \times 13 = 169 \)

### Step 2: Substitute the values into the equation
Now, we can substitute these values into the equation:
\[ 121 + (?)^2 + 169 = 1068 \]

### Step 3: Combine the constants
Next, we combine the constants \( 121 \) and \( 169 \):
\[ 121 + 169 = 290 \]
So, the equation now looks like:
\[ 290 + (?)^2 = 1068 \]

### Step 4: Isolate the square term
To isolate \( (?)^2 \), we subtract \( 290 \) from both sides:
\[ (?)^2 = 1068 - 290 \]

### Step 5: Perform the subtraction
Now, we perform the subtraction:
\[ 1068 - 290 = 778 \]
So, we have:
\[ (?)^2 = 778 \]

### Step 6: Take the square root
Finally, we take the square root of both sides to find \( ? \):
\[ ? = \sqrt{778} \]

### Step 7: Simplify the square root (if necessary)
The square root of \( 778 \) does not simplify to a whole number, so we can approximate it:
\[ ? \approx 27.9 \]

### Final Answer
Thus, the value that comes in place of the question mark is \( \sqrt{778} \) or approximately \( 27.9 \).

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