To solve the expression \((2 + \sqrt{3})(2 + \sqrt{2})\), we can use the distributive property (also known as the FOIL method for binomials) to expand it:

\[
(2 + \sqrt{3})(2 + \sqrt{2}) = 2 \cdot 2 + 2 \cdot \sqrt{2} + \sqrt{3} \cdot 2 + \sqrt{3} \cdot \sqrt{2}
\]

Now, let's compute each term:

1. \(2 \cdot 2 = 4\)
2. \(2 \cdot \sqrt{2} = 2\sqrt{2}\)
3. \(\sqrt{3} \cdot 2 = 2\sqrt{3}\)
4. \(\sqrt{3} \cdot \sqrt{2} = \sqrt{6}\)

Combining all these terms gives:

\[
4 + 2\sqrt{2} + 2\sqrt{3} + \sqrt{6}
\]

So, the expanded and simplified form of \((2 + \sqrt{3})(2 + \sqrt{2})\) is:

\[
\boxed{4 + 2\sqrt{2} + 2\sqrt{3} + \sqrt{6}}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you multiply two binomials using the FOIL method?
2. What are some properties of square roots that help in simplifying expressions?
3. How do you simplify expressions involving irrational numbers?
4. Can you explain the distributive property in more depth?
5. How would you multiply expressions involving cube roots instead of square roots?

**Tip:** When expanding expressions with square roots, remember that \(\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}\).

Explore how to expand and simplify the expression (2 + √3)(2 + √2) step-by-step with a detailed solution. This problem involves multiplication of binomials, square roots, and the distributive property. Suitable for high school students.

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