Evaluate :
`sqrt((5 + 2(21)/(25)) xx (0.169)/(1.6))`

Answer

To evaluate the expression \( \sqrt{(5 + \frac{2 \times 21}{25}) \times \frac{0.169}{1.6}} \), we will follow these steps:

### Step 1: Simplify the expression inside the square root
We start with the expression:
\[ \sqrt{5 + \frac{2 \times 21}{25} \times \frac{0.169}{1.6}} \]

### Step 2: Calculate \( \frac{2 \times 21}{25} \)
First, we calculate \( 2 \times 21 \):
\[ 2 \times 21 = 42 \]
Now, divide by 25:
\[ \frac{42}{25} = 1.68 \]

### Step 3: Calculate \( \frac{0.169}{1.6} \)
Next, we calculate \( \frac{0.169}{1.6} \). To do this, we can eliminate the decimal by multiplying both the numerator and the denominator by 1000:
\[ \frac{0.169 \times 1000}{1.6 \times 1000} = \frac{169}{1600} \]

### Step 4: Combine the results
Now we substitute back into the square root:
\[ \sqrt{5 + 1.68 \times \frac{169}{1600}} \]

### Step 5: Calculate \( 1.68 \times \frac{169}{1600} \)
Calculating this gives:
\[ 1.68 \times \frac{169}{1600} = \frac{1.68 \times 169}{1600} = \frac{283.52}{1600} \]

### Step 6: Add 5 to the result
Convert 5 into a fraction with a denominator of 1600:
\[ 5 = \frac{8000}{1600} \]
Now add:
\[ \frac{8000 + 283.52}{1600} = \frac{8283.52}{1600} \]

### Step 7: Take the square root
Now we take the square root:
\[ \sqrt{\frac{8283.52}{1600}} = \frac{\sqrt{8283.52}}{\sqrt{1600}} = \frac{\sqrt{8283.52}}{40} \]

### Step 8: Calculate \( \sqrt{8283.52} \)
Using a calculator, we find:
\[ \sqrt{8283.52} \approx 91 \]
Thus:
\[ \frac{91}{40} = 2.275 \]

### Final Answer
The final evaluated result is approximately:
\[ \sqrt{(5 + \frac{2 \times 21}{25}) \times \frac{0.169}{1.6}} \approx 2.275 \]