If ` 3a+(1)/(3a) = 2sqrt3` , evaluate:
` 3a- (1)/(3a)`

Answer

To solve the equation \( 3a + \frac{1}{3a} = 2\sqrt{3} \) and evaluate \( 3a - \frac{1}{3a} \), we can follow these steps:

### Step 1: Set up the equation
We start with the given equation:
\[ 3a + \frac{1}{3a} = 2\sqrt{3} \]

### Step 2: Use the identity
We will use the identity:
\[ (a - b)^2 = (a + b)^2 - 4ab \]
Here, let \( a = 3a \) and \( b = \frac{1}{3a} \).

### Step 3: Calculate \( (3a - \frac{1}{3a})^2 \)
Using the identity:
\[ (3a - \frac{1}{3a})^2 = (3a + \frac{1}{3a})^2 - 4 \cdot 3a \cdot \frac{1}{3a} \]

### Step 4: Substitute the known value
We know \( 3a + \frac{1}{3a} = 2\sqrt{3} \), so we can substitute this into the equation:
\[ (3a - \frac{1}{3a})^2 = (2\sqrt{3})^2 - 4 \]

### Step 5: Calculate \( (2\sqrt{3})^2 \)
Calculating \( (2\sqrt{3})^2 \):
\[ (2\sqrt{3})^2 = 4 \cdot 3 = 12 \]

### Step 6: Substitute back into the equation
Now substituting back:
\[ (3a - \frac{1}{3a})^2 = 12 - 4 \]
\[ (3a - \frac{1}{3a})^2 = 8 \]

### Step 7: Take the square root
Now we take the square root of both sides:
\[ 3a - \frac{1}{3a} = \sqrt{8} \]
\[ 3a - \frac{1}{3a} = 2\sqrt{2} \]

### Final Answer
Thus, the value of \( 3a - \frac{1}{3a} \) is:
\[ \boxed{2\sqrt{2}} \]