What will come in place of question mark (?) in the following questions ?
`sqrt(48 xx 28 xx 14 xx 6) -224 =?`

Options

A. 116
B. 111
C. 112
D. None of these

Answer

To solve the equation \( \sqrt{48 \times 28 \times 14 \times 6} - 224 = ? \), we will follow these steps:

### Step 1: Factor the numbers inside the square root
We can break down each number into its prime factors:
- \( 48 = 16 \times 3 = 4^2 \times 3 \)
- \( 28 = 14 \times 2 = 14 \times 2 \)
- \( 14 = 14 \)
- \( 6 = 2 \times 3 \)

### Step 2: Rewrite the expression
Now we can rewrite the expression inside the square root:
\[ \sqrt{48 \times 28 \times 14 \times 6} = \sqrt{(16 \times 3) \times (14 \times 2) \times 14 \times (2 \times 3)} \]

### Step 3: Combine the factors
Now we can combine the factors:
\[ = \sqrt{(16 \times 14^2 \times 3^2 \times 2^2)} \]

### Step 4: Simplify the square root
We can take the square root of each factor:
\[ = \sqrt{16} \times \sqrt{14^2} \times \sqrt{3^2} \times \sqrt{2^2} \]
\[ = 4 \times 14 \times 3 \times 2 \]

### Step 5: Calculate the product
Now we calculate the product:
\[ = 4 \times 14 = 56 \]
\[ = 56 \times 3 = 168 \]
\[ = 168 \times 2 = 336 \]

### Step 6: Subtract 224 from the result
Now we subtract 224 from 336:
\[ 336 - 224 = 112 \]

### Final Answer
Thus, the value that comes in place of the question mark (?) is:
\[ \boxed{112} \]