Compare the surds
(i) `A=sqrt(10)-sqrt(5),B=sqrt(19)-sqrt(14)`
(ii) `P=sqrt(10)+sqrt(5),Q=sqrt(8)+sqrt(7)`

Explanation

To compare the surds given in the question, we will follow a systematic approach.

### Part (i): Compare A and B

1. **Define A and B**:
- Let \( A = \sqrt{10} - \sqrt{5} \)
- Let \( B = \sqrt{19} - \sqrt{14} \)

2. **Square A and B**:
- Calculate \( A^2 \):
\[ A^2 = (\sqrt{10} - \sqrt{5})^2 = 10 + 5 - 2\sqrt{10 \cdot 5} = 15 - 2\sqrt{50} \]
- Calculate \( B^2 \):
\[ B^2 = (\sqrt{19} - \sqrt{14})^2 = 19 + 14 - 2\sqrt{19 \cdot 14} = 33 - 2\sqrt{266} \]

3. **Compare \( A^2 \) and \( B^2 \)**:
- We need to compare \( 15 - 2\sqrt{50} \) and \( 33 - 2\sqrt{266} \).
- Rearranging gives us:
\[ A^2 < B^2 \text{ if } 15 - 2\sqrt{50} < 33 - 2\sqrt{266} \]
- Simplifying this leads to:
\[ -2\sqrt{50} < 18 - 2\sqrt{266} \]
\[ 2\sqrt{266} - 2\sqrt{50} > 18 \]
\[ \sqrt{266} - \sqrt{50} > 9 \]

4. **Calculate \( \sqrt{266} \) and \( \sqrt{50} \)**:
- Approximate values:
\[ \sqrt{266} \approx 16.31 \quad \text{and} \quad \sqrt{50} \approx 7.07 \]
- Thus:
\[ 16.31 - 7.07 \approx 9.24 > 9 \]

5. **Conclusion for Part (i)**:
- Since \( A^2 < B^2 \), we conclude that \( A < B \).

### Part (ii): Compare P and Q

1. **Define P and Q**:
- Let \( P = \sqrt{10} + \sqrt{5} \)
- Let \( Q = \sqrt{8} + \sqrt{7} \)

2. **Square P and Q**:
- Calculate \( P^2 \):
\[ P^2 = (\sqrt{10} + \sqrt{5})^2 = 10 + 5 + 2\sqrt{10 \cdot 5} = 15 + 2\sqrt{50} \]
- Calculate \( Q^2 \):
\[ Q^2 = (\sqrt{8} + \sqrt{7})^2 = 8 + 7 + 2\sqrt{8 \cdot 7} = 15 + 2\sqrt{56} \]

3. **Compare \( P^2 \) and \( Q^2 \)**:
- We need to compare \( 15 + 2\sqrt{50} \) and \( 15 + 2\sqrt{56} \).
- Since both have the same constant term (15), we compare the square root terms:
\[ 2\sqrt{50} < 2\sqrt{56} \]
- Dividing by 2 gives:
\[ \sqrt{50} < \sqrt{56} \]

4. **Conclusion for Part (ii)**:
- Since \( P^2 < Q^2 \), we conclude that \( P < Q \).

### Final Results:
- For part (i): \( B > A \)
- For part (ii): \( Q > P \)