Which of the following statement (s) is /are True ?
I. `sqrt((64))+sqrt((0.0064))+sqrt((0.81))+sqrt((0.0081))=9.07`
II. `sqrt((0.010201))+sqrt((98.01))+sqrt((0.25))=11.51`

Options

A. Only I
B. Only II
C. Neither I nor II
D. Both I and II

Answer

To determine which of the statements is true, we will evaluate each statement step by step.

### Statement I:
\[ \sqrt{64} + \sqrt{0.0064} + \sqrt{0.81} + \sqrt{0.0081} = 9.07 \]

1. **Calculate \(\sqrt{64}\)**:
\[ \sqrt{64} = 8 \]

**Hint**: Recall that \(8 \times 8 = 64\).

2. **Calculate \(\sqrt{0.0064}\)**:
\[ \sqrt{0.0064} = \sqrt{\frac{64}{10000}} = \frac{\sqrt{64}}{\sqrt{10000}} = \frac{8}{100} = 0.08 \]

**Hint**: Remember that \(\sqrt{0.0064}\) can be simplified by rewriting it as \(\frac{64}{10000}\).

3. **Calculate \(\sqrt{0.81}\)**:
\[ \sqrt{0.81} = 0.9 \]

**Hint**: Recognize that \(0.9 \times 0.9 = 0.81\).

4. **Calculate \(\sqrt{0.0081}\)**:
\[ \sqrt{0.0081} = \sqrt{\frac{81}{10000}} = \frac{\sqrt{81}}{\sqrt{10000}} = \frac{9}{100} = 0.09 \]

**Hint**: Similar to the previous step, express \(0.0081\) as \(\frac{81}{10000}\).

5. **Add all the results**:
\[ 8 + 0.08 + 0.9 + 0.09 = 9.07 \]

**Hint**: Make sure to align the decimal points when adding.

### Conclusion for Statement I:
The first statement is **True**.

---

### Statement II:
\[ \sqrt{0.010201} + \sqrt{98.01} + \sqrt{0.25} = 11.51 \]

1. **Calculate \(\sqrt{0.010201}\)**:
\[ \sqrt{0.010201} = \sqrt{\frac{10201}{1000000}} = \frac{\sqrt{10201}}{\sqrt{1000000}} = \frac{101}{1000} = 0.101 \]

**Hint**: Recognize that \(10201\) is \(101^2\).

2. **Calculate \(\sqrt{98.01}\)**:
\[ \sqrt{98.01} = \sqrt{(99 - 0.99)} \approx 9.9 \quad \text{(since \(99\) is close to \(98.01\))} \]

**Hint**: Use approximation or recognize that \(9.9^2\) is close to \(98.01\).

3. **Calculate \(\sqrt{0.25}\)**:
\[ \sqrt{0.25} = 0.5 \]

**Hint**: Remember that \(0.5 \times 0.5 = 0.25\).

4. **Add all the results**:
\[ 0.101 + 9.9 + 0.5 = 10.501 \]

**Hint**: Carefully add the decimal values together.

### Conclusion for Statement II:
The second statement is **False**.

### Final Answer:
Only the first statement is true.