What should come in place of the question mark (?) in the following questions:
`264 -: sqrt576 + (11)^2 + 12 = (?)^2` . Options are (a) `sqrt12` (b) 144 (c) 12 (d) `(132)^2` .

Options

A. `sqrt12`
B. 144
C. 12
D. `(132)^2`

Answer

To solve the equation \( 264 \div \sqrt{576} + (11)^2 + 12 = (?)^2 \), we will follow these steps:

### Step 1: Calculate \( \sqrt{576} \)
The square root of 576 can be calculated as follows:
\[ \sqrt{576} = 24 \]

### Step 2: Substitute \( \sqrt{576} \) back into the equation
Now we can substitute this value back into the equation:
\[ 264 \div 24 + (11)^2 + 12 = (?)^2 \]

### Step 3: Calculate \( 264 \div 24 \)
Now, we perform the division:
\[ 264 \div 24 = 11 \]

### Step 4: Calculate \( (11)^2 \)
Next, we calculate \( (11)^2 \):
\[ (11)^2 = 121 \]

### Step 5: Add the results together
Now we can add all the terms together:
\[ 11 + 121 + 12 = 144 \]

### Step 6: Set the equation equal to \( (?)^2 \)
Now we have:
\[ 144 = (?)^2 \]

### Step 7: Solve for \( ? \)
To find \( ? \), we take the square root of both sides:
\[ ? = \sqrt{144} = 12 \]

Thus, the value that comes in place of the question mark is:
\[ \boxed{12} \]