Given that `sqrt(5625) =75` , the value of `sqrt(0.5625) + sqrt(56.25)` is:

Options

A. `82.5`
B. `0.75`
C. `8.25`
D. `75.05`

Answer

To solve the problem, we need to find the value of \( \sqrt{0.5625} + \sqrt{56.25} \) given that \( \sqrt{5625} = 75 \).

### Step-by-step Solution:

1. **Express \( 0.5625 \) and \( 56.25 \) in terms of \( 5625 \)**:
- We can rewrite \( 0.5625 \) as \( \frac{5625}{10000} \) and \( 56.25 \) as \( \frac{5625}{100} \).

2. **Apply the square root property**:
- Using the property of square roots, we have:
\[ \sqrt{0.5625} = \sqrt{\frac{5625}{10000}} = \frac{\sqrt{5625}}{\sqrt{10000}} = \frac{\sqrt{5625}}{100} \]
- Similarly,
\[ \sqrt{56.25} = \sqrt{\frac{5625}{100}} = \frac{\sqrt{5625}}{\sqrt{100}} = \frac{\sqrt{5625}}{10} \]

3. **Substitute the value of \( \sqrt{5625} \)**:
- Since \( \sqrt{5625} = 75 \), we can substitute this value:
\[ \sqrt{0.5625} = \frac{75}{100} = 0.75 \]
\[ \sqrt{56.25} = \frac{75}{10} = 7.5 \]

4. **Add the two square roots**:
- Now, we can add the two results:
\[ \sqrt{0.5625} + \sqrt{56.25} = 0.75 + 7.5 = 8.25 \]

### Final Answer:
The value of \( \sqrt{0.5625} + \sqrt{56.25} \) is \( 8.25 \).

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