Do as directed:
(i) Add : `sqrt(125 + 2 sqrt(27)` and `- 5 sqrt(5) - sqrt(3)`
(ii) Add: `sqrt(7) - sqrt(11)` and `sqrt(5) - sqrt(11) + sqrt(13)`
(iii) Multiply : `2 sqrt(2)` by `5 sqrt(2)`
(iv) Multiply : `(-3 + sqrt(5))` by 3
(v) Divide : `7 sqrt(5)` by `- 14 sqrt(125)`
Divide : `7 sqrt(5)` by `-14 sqrt(125)`
(vi) Divide : `2 sqrt(216) - 3 sqrt(27)` by 3

Answer

Let's solve each part of the question step by step.

### Part (i): Add `sqrt(125 + 2 sqrt(27)` and `- 5 sqrt(5) - sqrt(3)`

1. **Simplify `sqrt(125)`**:
- `sqrt(125) = sqrt(25 * 5) = sqrt(25) * sqrt(5) = 5sqrt(5)`

2. **Simplify `sqrt(27)`**:
- `sqrt(27) = sqrt(9 * 3) = sqrt(9) * sqrt(3) = 3sqrt(3)`

3. **Substituting back into the expression**:
- `sqrt(125 + 2sqrt(27)) = sqrt(5sqrt(5) + 2 * 3sqrt(3)) = sqrt(5sqrt(5) + 6sqrt(3))`

4. **Now, add `-5sqrt(5) - sqrt(3)`**:
- Combine like terms:
- `5sqrt(5) - 5sqrt(5) + 6sqrt(3) - sqrt(3) = 0 + 5sqrt(3)`

5. **Final Result**:
- The answer is `5sqrt(3)`.