If `sqrt(5329)=73`, then the value of `sqrt(5329)+sqrt(53.29)+sqrt(0.5329)+sqrt(0.005329)+sqrt(0.00005329)` is

Options

A. `81.1003`
B. `81.0113`
C. `81.1103`
D. `81.1013`

Answer

To solve the problem step by step, we start with the information given:

1. We know that \( \sqrt{5329} = 73 \).

Now, let's calculate the other square roots in the expression:

2. **Calculate \( \sqrt{53.29} \)**:
- We can express \( 53.29 \) as \( \frac{5329}{100} \).
- Therefore, \( \sqrt{53.29} = \sqrt{\frac{5329}{100}} = \frac{\sqrt{5329}}{\sqrt{100}} = \frac{73}{10} = 7.3 \).

3. **Calculate \( \sqrt{0.5329} \)**:
- We can express \( 0.5329 \) as \( \frac{5329}{10000} \).
- Therefore, \( \sqrt{0.5329} = \sqrt{\frac{5329}{10000}} = \frac{\sqrt{5329}}{\sqrt{10000}} = \frac{73}{100} = 0.73 \).

4. **Calculate \( \sqrt{0.005329} \)**:
- We can express \( 0.005329 \) as \( \frac{5329}{1000000} \).
- Therefore, \( \sqrt{0.005329} = \sqrt{\frac{5329}{1000000}} = \frac{\sqrt{5329}}{\sqrt{1000000}} = \frac{73}{1000} = 0.073 \).

5. **Calculate \( \sqrt{0.00005329} \)**:
- We can express \( 0.00005329 \) as \( \frac{5329}{100000000} \).
- Therefore, \( \sqrt{0.00005329} = \sqrt{\frac{5329}{100000000}} = \frac{\sqrt{5329}}{\sqrt{100000000}} = \frac{73}{10000} = 0.0073 \).

Now we can sum all these values:

6. **Sum the values**:
\[ \sqrt{5329} + \sqrt{53.29} + \sqrt{0.5329} + \sqrt{0.005329} + \sqrt{0.00005329} = 73 + 7.3 + 0.73 + 0.073 + 0.0073 \]

Let's calculate this step by step:
- First, add \( 73 + 7.3 = 80.3 \).
- Next, add \( 80.3 + 0.73 = 81.03 \).
- Then, add \( 81.03 + 0.073 = 81.103 \).
- Finally, add \( 81.103 + 0.0073 = 81.1103 \).

Thus, the final result is:
\[ \sqrt{5329} + \sqrt{53.29} + \sqrt{0.5329} + \sqrt{0.005329} + \sqrt{0.00005329} = 81.1103 \]