To solve $(5 + \sqrt{5})(2 + \sqrt{5})$, we can use the distributive property (also known as the FOIL method for binomials):

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

Now, calculate each term:

1. $5 \cdot 2 = 10$
2. $5 \cdot \sqrt{5} = 5\sqrt{5}$
3. $\sqrt{5} \cdot 2 = 2\sqrt{5}$
4. $\sqrt{5} \cdot \sqrt{5} = 5$

Now, combine all the terms:

$10 + 5\sqrt{5} + 2\sqrt{5} + 5$

Simplify:

$(10 + 5) + (5\sqrt{5} + 2\sqrt{5}) = 15 + 7\sqrt{5}$

Thus, the result is:

$15 + 7\sqrt{5}$

Would you like further details or have any other questions?

Here are 5 related questions to expand your understanding:

1. What is the general rule for multiplying binomials?
2. How would you multiply $(a + \sqrt{b})(c + \sqrt{d})$?
3. What happens when you multiply two conjugates like $(a + \sqrt{b})(a - \sqrt{b})$?
4. How do you simplify expressions involving square roots?
5. How would you apply the distributive property to three binomials?

Tip: When multiplying terms with square roots, remember that $\sqrt{a} \times \sqrt{a} = a$.