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. 37.167

Answer

To find the value of \( \sqrt{1.3} + \sqrt{1300} + \sqrt{0.013} \), we can break down each term using the approximations given for \( \sqrt{13} \) and \( \sqrt{130} \).

### Step 1: Calculate \( \sqrt{1.3} \)
We can express \( 1.3 \) as \( \frac{13}{10} \):
\[ \sqrt{1.3} = \sqrt{\frac{13}{10}} = \frac{\sqrt{13}}{\sqrt{10}} \]
Since \( \sqrt{10} \) is approximately \( 3.162 \) (since \( \sqrt{10} \approx \sqrt{(3.16)^2} \)), we can substitute:
\[ \sqrt{1.3} \approx \frac{3.605}{3.162} \approx 1.139 \]

### Step 2: Calculate \( \sqrt{1300} \)
We can express \( 1300 \) as \( 130 \times 10 \):
\[ \sqrt{1300} = \sqrt{130 \times 10} = \sqrt{130} \times \sqrt{10} \]
Using the approximation \( \sqrt{130} \approx 11.40 \):
\[ \sqrt{1300} \approx 11.40 \times 3.162 \approx 36.1 \]

### Step 3: Calculate \( \sqrt{0.013} \)
We can express \( 0.013 \) as \( \frac{13}{1000} \):
\[ \sqrt{0.013} = \sqrt{\frac{13}{1000}} = \frac{\sqrt{13}}{\sqrt{1000}} \]
Since \( \sqrt{1000} \approx 31.622 \):
\[ \sqrt{0.013} \approx \frac{3.605}{31.622} \approx 0.114 \]

### Step 4: Combine all the results
Now, we can add all three results together:
\[ \sqrt{1.3} + \sqrt{1300} + \sqrt{0.013} \approx 1.139 + 36.1 + 0.114 \]
Calculating this gives:
\[ 1.139 + 36.1 + 0.114 \approx 37.353 \]

### Final Answer
Thus, the value of \( \sqrt{1.3} + \sqrt{1300} + \sqrt{0.013} \) is approximately \( 37.353 \).

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