What will come in place of question mark (?) in the given questions?
`(36-:sqrt18xxsqrt6)-:3=?`

Options

A. `6sqrt3`
B. `6sqrt2`
C. `4sqrt3`
D. `4/sqrt2`

Answer

To solve the equation \( (36 \div \sqrt{18} \times \sqrt{6}) \div 3 = ? \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Identify the Expression**:
The expression we need to solve is:
\[ (36 \div \sqrt{18} \times \sqrt{6}) \div 3 \]

2. **Calculate the Square Roots**:
We first need to simplify \( \sqrt{18} \) and \( \sqrt{6} \):
\[ \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \]
\[ \sqrt{6} = \sqrt{6} \]

3. **Substitute Back into the Expression**:
Now substitute the square roots back into the expression:
\[ (36 \div (3\sqrt{2}) \times \sqrt{6}) \div 3 \]

4. **Simplify Inside the Bracket**:
First, calculate \( 36 \div (3\sqrt{2}) \):
\[ 36 \div (3\sqrt{2}) = \frac{36}{3\sqrt{2}} = \frac{12}{\sqrt{2}} \]

5. **Multiply by \( \sqrt{6} \)**:
Now multiply this result by \( \sqrt{6} \):
\[ \frac{12}{\sqrt{2}} \times \sqrt{6} = \frac{12\sqrt{6}}{\sqrt{2}} = 12 \times \sqrt{\frac{6}{2}} = 12 \times \sqrt{3} = 12\sqrt{3} \]

6. **Divide by 3**:
Now divide by 3:
\[ \frac{12\sqrt{3}}{3} = 4\sqrt{3} \]

7. **Final Answer**:
Therefore, the value that comes in place of the question mark (?) is:
\[ 4\sqrt{3} \]