Simplify each of the following expressions: (i) `(3+sqrt(3))(2+sqrt(2))` (ii) `(3+sqrt(3))(3-sqrt(3))` (iii) `(sqrt(5)+sqrt(2))^2`(iv) `(sqrt(5)-sqrt(2))(sqrt(5)+sqrt(2))`

Explanation

Let's simplify each of the given expressions step by step.

### (i) Simplify `(3 + √3)(2 + √2)`

1. **Distribute the terms**:
\[ (3 + \sqrt{3})(2 + \sqrt{2}) = 3 \cdot 2 + 3 \cdot \sqrt{2} + \sqrt{3} \cdot 2 + \sqrt{3} \cdot \sqrt{2} \]
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