We can expand $(\sqrt{3} - \sqrt{5})^2$ using the formula for the square of a binomial, which is:

$(a - b)^2 = a^2 - 2ab + b^2$

Here, $a = \sqrt{3}$ and $b = \sqrt{5}$.

Now, apply the formula:

$(\sqrt{3} - \sqrt{5})^2 = (\sqrt{3})^2 - 2 \cdot \sqrt{3} \cdot \sqrt{5} + (\sqrt{5})^2$

Simplify each term:

$= 3 - 2\sqrt{15} + 5$

Now combine the constants:

$= 8 - 2\sqrt{15}$

So, the result is:

$(\sqrt{3} - \sqrt{5})^2 = 8 - 2\sqrt{15}$

Would you like more details on how the square of binomials works?

Here are 5 related questions for practice:

1. Expand $(\sqrt{2} - \sqrt{7})^2$.
2. Simplify $(\sqrt{6} + \sqrt{2})^2$.
3. What is $(a - b)^2$ when $a = \sqrt{11}$ and $b = \sqrt{3}$?
4. Expand $(3 - \sqrt{2})^2$.
5. What is the general form of $(a + b)^2$?

Tip: When dealing with square roots in expressions, apply basic algebraic identities carefully to ensure no mistakes in simplification.