Given that `sqrt(24025)=155`, then
`sqrt(240.25)+sqrt(2.4025)+sqrt(0.024025)+sqrt(0.00024025)` is equal to

Options

A. `16.2205`
B. `16.2402`
C. `17.2205`
D. `155.2205`

Answer

To solve the expression \( \sqrt{240.25} + \sqrt{2.4025} + \sqrt{0.024025} + \sqrt{0.00024025} \), we will use the fact that \( \sqrt{24025} = 155 \) and apply the properties of square roots.

### Step-by-Step Solution:

1. **Calculate \( \sqrt{240.25} \)**:
- Rewrite \( 240.25 \) as \( \frac{24025}{100} \) (since there are 2 digits after the decimal).
- Therefore, \( \sqrt{240.25} = \sqrt{\frac{24025}{100}} = \frac{\sqrt{24025}}{\sqrt{100}} = \frac{155}{10} = 15.5 \).

2. **Calculate \( \sqrt{2.4025} \)**:
- Rewrite \( 2.4025 \) as \( \frac{24025}{10000} \) (since there are 4 digits after the decimal).
- Thus, \( \sqrt{2.4025} = \sqrt{\frac{24025}{10000}} = \frac{\sqrt{24025}}{\sqrt{10000}} = \frac{155}{100} = 1.55 \).

3. **Calculate \( \sqrt{0.024025} \)**:
- Rewrite \( 0.024025 \) as \( \frac{24025}{1000000} \) (since there are 6 digits after the decimal).
- Therefore, \( \sqrt{0.024025} = \sqrt{\frac{24025}{1000000}} = \frac{\sqrt{24025}}{\sqrt{1000000}} = \frac{155}{1000} = 0.155 \).

4. **Calculate \( \sqrt{0.00024025} \)**:
- Rewrite \( 0.00024025 \) as \( \frac{24025}{100000000} \) (since there are 8 digits after the decimal).
- Thus, \( \sqrt{0.00024025} = \sqrt{\frac{24025}{100000000}} = \frac{\sqrt{24025}}{\sqrt{100000000}} = \frac{155}{10000} = 0.0155 \).

5. **Add all the values together**:
- Now we sum up all the calculated square roots:
\[ 15.5 + 1.55 + 0.155 + 0.0155 \]

- Performing the addition:
\[ 15.5 + 1.55 = 17.05 \]
\[ 17.05 + 0.155 = 17.205 \]
\[ 17.205 + 0.0155 = 17.2205 \]

### Final Answer:
The value of \( \sqrt{240.25} + \sqrt{2.4025} + \sqrt{0.024025} + \sqrt{0.00024025} \) is \( 17.2205 \).

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