The problem asks to simplify the expression $\left(\sqrt{5} + \sqrt{2}\right)\left(\sqrt{5} - \sqrt{2}\right)$.

This expression can be simplified using the difference of squares formula, which is given by:

$(a + b)(a - b) = a^2 - b^2$

Here, $a = \sqrt{5}$ and $b = \sqrt{2}$. Substituting these values into the formula:

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

Now, simplify the squares:

$(\sqrt{5})^2 = 5 \quad \text{and} \quad (\sqrt{2})^2 = 2$

So, the expression simplifies to:

$5 - 2 = 3$

Thus, the simplified value of the expression is 3.

Looking at the answer choices provided in the image:

• Option B shows $\sqrt{9}$, which simplifies to 3. Hence, the correct answer is B.

Would you like more details or have any questions? Here are some related questions to expand your understanding:

1. How would you simplify an expression like $(\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b})$ if $a$ and $b$ are not perfect squares?
2. What is the general formula for the difference of squares, and how can it be applied in other contexts?
3. Can the difference of squares method be used to simplify expressions involving cube roots?
4. What are some real-world applications of the difference of squares in mathematics?
5. How would you approach simplifying a similar expression if it included a different operation, like addition instead of multiplication?

Tip: When simplifying expressions involving radicals, look for opportunities to use identities like the difference of squares, as they can significantly simplify the process.