Assume that `sqrt(13) = 3.605` (approximately) `sqrt(130) = 11.40` (approximately)
Find the value of : `sqrt(1.3) + sqrt(1300) + sqrt(0.013)`

Options

A. 36.164
B. 36.304
C. 37.304
D. 37.164

Answer

To find the value of \( \sqrt{1.3} + \sqrt{1300} + \sqrt{0.013} \), we can simplify each term step by step using the approximations provided.

### Step 1: Simplify \( \sqrt{1.3} \)
We can express \( \sqrt{1.3} \) as:
\[ \sqrt{1.3} = \sqrt{\frac{13}{10}} = \frac{\sqrt{13}}{\sqrt{10}} \]
Using the approximations given:
- \( \sqrt{13} \approx 3.605 \)
- \( \sqrt{10} \approx 3.162 \) (since \( \sqrt{10} \) is not given, we can estimate it)

Calculating \( \sqrt{1.3} \):
\[ \sqrt{1.3} \approx \frac{3.605}{3.162} \approx 1.139 \]

### Step 2: Simplify \( \sqrt{1300} \)
We can express \( \sqrt{1300} \) as:
\[ \sqrt{1300} = \sqrt{13 \times 100} = \sqrt{13} \times \sqrt{100} = \sqrt{13} \times 10 \]
Calculating \( \sqrt{1300} \):
\[ \sqrt{1300} \approx 3.605 \times 10 = 36.05 \]

### Step 3: Simplify \( \sqrt{0.013} \)
We can express \( \sqrt{0.013} \) as:
\[ \sqrt{0.013} = \sqrt{\frac{13}{1000}} = \frac{\sqrt{13}}{\sqrt{1000}} \]
Using the approximation:
- \( \sqrt{1000} = \sqrt{10^3} = 10 \times \sqrt{10} \approx 10 \times 3.162 = 31.62 \)

Calculating \( \sqrt{0.013} \):
\[ \sqrt{0.013} \approx \frac{3.605}{31.62} \approx 0.114 \]

### Step 4: Combine the results
Now we can add the three results together:
\[ \sqrt{1.3} + \sqrt{1300} + \sqrt{0.013} \approx 1.139 + 36.05 + 0.114 \]
Calculating the sum:
\[ 1.139 + 36.05 + 0.114 \approx 37.303 \]

### Final Answer
Thus, the value of \( \sqrt{1.3} + \sqrt{1300} + \sqrt{0.013} \) is approximately:
\[ \boxed{37.304} \]