Given that `sqrt(1225)=35`, find the value of `sqrt(12.25)+sqrt(0.1225)+sqrt(0.001225)`

Options

A. `0.3885`
B. `388.5`
C. `38.85`
D. `3.885`

Answer

To solve the problem \( \sqrt{12.25} + \sqrt{0.1225} + \sqrt{0.001225} \) given that \( \sqrt{1225} = 35 \), we can follow these steps:

### Step 1: Rewrite the square roots in terms of 1225
We know that:
- \( \sqrt{12.25} = \sqrt{\frac{1225}{100}} \)
- \( \sqrt{0.1225} = \sqrt{\frac{1225}{10000}} \)
- \( \sqrt{0.001225} = \sqrt{\frac{1225}{1000000}} \)

### Step 2: Simplify each square root
Using the property of square roots \( \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} \):
1. \( \sqrt{12.25} = \frac{\sqrt{1225}}{\sqrt{100}} = \frac{35}{10} = 3.5 \)
2. \( \sqrt{0.1225} = \frac{\sqrt{1225}}{\sqrt{10000}} = \frac{35}{100} = 0.35 \)
3. \( \sqrt{0.001225} = \frac{\sqrt{1225}}{\sqrt{1000000}} = \frac{35}{1000} = 0.035 \)

### Step 3: Add the simplified square roots
Now, we can add the results from Step 2:
\[ 3.5 + 0.35 + 0.035 \]

### Step 4: Perform the addition
1. First, add \( 3.5 + 0.35 = 3.85 \)
2. Then, add \( 3.85 + 0.035 = 3.885 \)

### Final Answer
Thus, the value of \( \sqrt{12.25} + \sqrt{0.1225} + \sqrt{0.001225} \) is \( \boxed{3.885} \).

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