`2sqrt3-sqrt3-3sqrt3+sqrt(12)` is equal to

Options

A. `6sqrt3`
B. `5sqrt3`
C. 0
D. 1

Answer

To solve the expression \(2\sqrt{3} - \sqrt{3} - 3\sqrt{3} + \sqrt{12}\), we can follow these steps:

### Step 1: Simplify the square root
First, simplify \(\sqrt{12}\):
\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]

### Step 2: Substitute back into the expression
Now, substitute \(\sqrt{12}\) back into the expression:
\[ 2\sqrt{3} - \sqrt{3} - 3\sqrt{3} + 2\sqrt{3} \]

### Step 3: Combine like terms
Now, combine all the terms involving \(\sqrt{3}\):
\[ (2\sqrt{3} + 2\sqrt{3}) - \sqrt{3} - 3\sqrt{3} = 4\sqrt{3} - \sqrt{3} - 3\sqrt{3} \]

### Step 4: Further simplify
Combine the terms:
\[ 4\sqrt{3} - \sqrt{3} - 3\sqrt{3} = 4\sqrt{3} - 4\sqrt{3} = 0 \]

### Final Answer
Thus, the expression simplifies to:
\[ \boxed{0} \]