If `(102)^(2)` = 10404 then, the value of `sqrt(104.04) + sqrt(1.0404) + sqrt(0.010404)` is equal to

Options

A. 0.306
B. 0.0306
C. 11.122
D. 11.322

Answer

To solve the problem, we start with the given information that \( (102)^2 = 10404 \). We need to find the value of \( \sqrt{104.04} + \sqrt{1.0404} + \sqrt{0.010404} \).

### Step-by-Step Solution:

1. **Rewrite the square roots using the given square**:
- We know \( 10404 = (102)^2 \).
- Therefore, we can express the square roots in terms of \( 102 \):
\[ \sqrt{104.04} = \sqrt{\frac{10404}{100}} = \frac{\sqrt{10404}}{\sqrt{100}} = \frac{102}{10} = 10.2 \]

2. **Calculate \( \sqrt{1.0404} \)**:
- Similarly, we can express \( 1.0404 \):
\[ \sqrt{1.0404} = \sqrt{\frac{10404}{10000}} = \frac{\sqrt{10404}}{\sqrt{10000}} = \frac{102}{100} = 1.02 \]

3. **Calculate \( \sqrt{0.010404} \)**:
- Now, for \( 0.010404 \):
\[ \sqrt{0.010404} = \sqrt{\frac{10404}{1000000}} = \frac{\sqrt{10404}}{\sqrt{1000000}} = \frac{102}{1000} = 0.102 \]

4. **Add the results together**:
- Now we can add all the square roots together:
\[ \sqrt{104.04} + \sqrt{1.0404} + \sqrt{0.010404} = 10.2 + 1.02 + 0.102 \]

5. **Perform the final addition**:
- Adding these values:
\[ 10.2 + 1.02 = 11.22 \]
\[ 11.22 + 0.102 = 11.322 \]

### Final Answer:
Thus, the value of \( \sqrt{104.04} + \sqrt{1.0404} + \sqrt{0.010404} \) is \( 11.322 \).

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