Evaluate :
`sqrt(1(4)/(5) xx 14(21)/(44) xx 2(7)/(55))`

Answer

To evaluate the expression \( \sqrt{\frac{1}{5} \times \frac{14}{44} \times \frac{2}{55}} \), we will follow these steps:

### Step 1: Simplify the fractions
First, we simplify each fraction in the expression:
- \( \frac{14}{44} \) can be simplified by dividing both the numerator and the denominator by 2:
\[ \frac{14 \div 2}{44 \div 2} = \frac{7}{22} \]
- So, the expression now looks like:
\[ \sqrt{\frac{1}{5} \times \frac{7}{22} \times \frac{2}{55}} \]

### Step 2: Multiply the fractions
Next, we multiply the fractions together:
\[ \frac{1 \times 7 \times 2}{5 \times 22 \times 55} \]
Calculating the numerator:
\[ 1 \times 7 \times 2 = 14 \]
Calculating the denominator:
\[ 5 \times 22 = 110 \quad \text{and} \quad 110 \times 55 = 6050 \]
So, we have:
\[ \sqrt{\frac{14}{6050}} \]

### Step 3: Simplify the fraction under the square root
Now, we can simplify \( \frac{14}{6050} \):
- Both 14 and 6050 can be divided by 2:
\[ \frac{14 \div 2}{6050 \div 2} = \frac{7}{3025} \]
Thus, we have:
\[ \sqrt{\frac{7}{3025}} \]

### Step 4: Separate the square root
We can separate the square root of the fraction:
\[ \sqrt{7} \div \sqrt{3025} \]

### Step 5: Calculate the square root of 3025
Next, we find \( \sqrt{3025} \):
- Since \( 3025 = 55^2 \), we have:
\[ \sqrt{3025} = 55 \]
So, the expression simplifies to:
\[ \frac{\sqrt{7}}{55} \]

### Step 6: Final evaluation
Now, we can evaluate \( \sqrt{7} \) approximately:
- \( \sqrt{7} \approx 2.64575 \)
Thus:
\[ \frac{2.64575}{55} \approx 0.0481 \]

### Final Answer
Therefore, the final answer is:
\[ \sqrt{\frac{1}{5} \times \frac{14}{44} \times \frac{2}{55}} \approx 0.0481 \]