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.

Learn how to expand and simplify (√3 - √5)² step by step using the binomial expansion formula. This problem involves simplifying radicals and combining constants. Suitable for students in Grades 9-11.

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