Evaluate the square root of `(0.342xx0.684)/(0.000342xx0.000171)`

Answer

To evaluate the square root of \((0.342 \times 0.684) / (0.000342 \times 0.000171)\), we will follow these steps:

### Step 1: Remove the decimals
First, we can simplify the expression by removing the decimals.

- The numerator is \(0.342 \times 0.684\).
- The denominator is \(0.000342 \times 0.000171\).

To remove the decimals:
- For \(0.342\), we can multiply by \(1000\) to get \(342\).
- For \(0.684\), we can also multiply by \(1000\) to get \(684\).
- For \(0.000342\), we multiply by \(1000000\) to get \(342\).
- For \(0.000171\), we multiply by \(1000000\) to get \(171\).

Thus, the expression becomes:
\[ \frac{342 \times 684}{342 \times 171} \]

### Step 2: Simplify the expression
Now, we can simplify the expression:
\[ \frac{342 \times 684}{342 \times 171} = \frac{684}{171} \]

### Step 3: Perform the division
Next, we divide \(684\) by \(171\):
\[ 684 \div 171 = 4 \]

### Step 4: Take the square root
Now we take the square root of \(4\):
\[ \sqrt{4} = 2 \]

### Step 5: Consider the powers of ten
Since we initially multiplied both the numerator and denominator by \(1000\) and \(1000000\) respectively, we need to account for the powers of ten. The total power of ten from the numerator is \(3\) (from \(1000\)) and from the denominator is \(6\) (from \(1000000\)).

Thus, we have:
\[ \sqrt{10^{3-6}} = \sqrt{10^{-3}} = \frac{1}{\sqrt{1000}} = \frac{1}{31.62} \approx 0.0316 \]

### Final Answer
Combining the results, we have:
\[ 2 \times 0.0316 = 0.0632 \]

So the final answer is:
\[ \sqrt{\frac{0.342 \times 0.684}{0.000342 \times 0.000171}} \approx 0.0632 \]