The given expression is:

$(\sqrt{5} + 2)(\sqrt{5} - 2)$

This is in the form of a difference of squares, $(a + b)(a - b) = a^2 - b^2$.

Here:

• $a = \sqrt{5}$
• $b = 2$

Substitute these into the formula:

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

Now calculate:

$(\sqrt{5})^2 = 5, \quad 2^2 = 4$

$(\sqrt{5} + 2)(\sqrt{5} - 2) = 5 - 4 = 1$

Final Answer:

$1$

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Would you like me to break this down further or explain another similar concept? Here are some related questions for exploration:

1. What are the properties of the difference of squares?
2. How do you expand expressions like $(a+b)^2$?
3. What is the geometric interpretation of $\sqrt{5}$?
4. Can you solve $x^2 - 5 = 0$ using radicals?
5. How does this apply to simplifying rational expressions?

Tip:

The difference of squares formula simplifies many quadratic expressions efficiently. Look for it when terms resemble $(a+b)(a-b)$.