Simplify the following expressions :
(a) `(sqrt(3)+sqrt(5))^(2)`
(b) `(sqrt(5)-sqrt(2))^(2)`

Answer

Let's simplify the given expressions step by step.

### Part (a): Simplify \((\sqrt{3} + \sqrt{5})^2\)

1. **Identify the formula**: We will use the formula for the square of a binomial, which states:
\[ (a + b)^2 = a^2 + 2ab + b^2 \]
Here, let \(a = \sqrt{3}\) and \(b = \sqrt{5}\).

2. **Apply the formula**:
\[ (\sqrt{3} + \sqrt{5})^2 = (\sqrt{3})^2 + 2(\sqrt{3})(\sqrt{5}) + (\sqrt{5})^2 \]

3. **Calculate each term**:
- \((\sqrt{3})^2 = 3\)
- \((\sqrt{5})^2 = 5\)
- \(2(\sqrt{3})(\sqrt{5}) = 2\sqrt{15}\)

4. **Combine the results**:
\[ 3 + 5 + 2\sqrt{15} = 8 + 2\sqrt{15} \]

Thus, the simplified expression for part (a) is:
\[ \boxed{8 + 2\sqrt{15}} \]