`sqrt((2704)/(81))=?`

Answer

To solve the question \(\sqrt{\frac{2704}{81}}\), we can follow these steps:

### Step 1: Rewrite the expression
We start by rewriting the square root of the fraction:
\[ \sqrt{\frac{2704}{81}} = \frac{\sqrt{2704}}{\sqrt{81}} \]

### Step 2: Calculate \(\sqrt{81}\)
Next, we calculate the square root of the denominator:
\[ \sqrt{81} = 9 \]

### Step 3: Calculate \(\sqrt{2704}\)
Now we need to find the square root of the numerator. We can check if 2704 is a perfect square.

To find \(\sqrt{2704}\), we can use prime factorization or check for perfect squares. After checking, we find:
\[ \sqrt{2704} = 52 \]

### Step 4: Combine the results
Now we can substitute our results back into the expression:
\[ \frac{\sqrt{2704}}{\sqrt{81}} = \frac{52}{9} \]

### Step 5: Final answer
Thus, the final answer is:
\[ \sqrt{\frac{2704}{81}} = \frac{52}{9} \]