Find the value of the expression $$(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})$$.

Explanation:

We need to find the value of the expression $$(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})$$. This expression is in the form of $$(a-b)(a+b)$$, which is a difference of squares and simplifies to $$a^2 - b^2$$.

Step-by-step solution:

1. Identify 'a' and 'b' in the expression. Here, $$a = \sqrt{5}$$ and $$b = \sqrt{2}$$.
2. Apply the difference of squares formula: $$(a-b)(a+b) = a^2 - b^2$$.
3. Substitute the values of 'a' and 'b' into the formula: $$(\sqrt{5})^2 - (\sqrt{2})^2$$.
4. Calculate the squares: $$(\sqrt{5})^2 = 5$$ and $$(\sqrt{2})^2 = 2$$.
5. Subtract the results: $$5 - 2 = 3$$.

Answer: 3