To solve the given expression $\sqrt{2} \sqrt{8 \& 2}$, let's first clarify the interpretation of the notation $\sqrt{8 \& 2}$. Assuming that $8 \& 2$ means multiplying $8$ and $2$, the expression simplifies as follows:

$\sqrt{2} \times \sqrt{8 \times 2}$

Next, calculate the product inside the square root:

$8 \times 2 = 16$

Now, substitute it back into the expression:

$\sqrt{2} \times \sqrt{16}$

Since $\sqrt{16} = 4$, the expression becomes:

$\sqrt{2} \times 4$

This simplifies to:

$4 \sqrt{2}$

Since none of the given options directly match $4 \sqrt{2}$, it seems like we might need to reconsider the interpretation of the original notation or the expression itself. However, if the intention is to match one of the given options based on a specific convention, further clarification would be needed.

If you want to discuss this further or have any questions, let me know! Meanwhile, here are some related questions you might find interesting:

1. What is the exact value of $\sqrt{2}$?
2. How do you simplify expressions involving square roots?
3. What is the square root of a product of two numbers?
4. Can you explain how to calculate the square root of a fraction?
5. What is the relationship between square roots and exponents?
6. How does the distributive property apply to square roots?
7. How do you rationalize the denominator in a square root expression?
8. What are the key properties of square roots?

Tip: When working with square roots, always ensure to simplify the expression as much as possible before comparing it with given options.