The question from your image asks for the result of $4\sqrt{10} \times \sqrt{2}$. We solve this by using the properties of square roots:

$4\sqrt{10} \times \sqrt{2} = 4\sqrt{10 \times 2} = 4\sqrt{20}$

We can simplify $\sqrt{20}$ further since $20 = 4 \times 5$ and $\sqrt{4} = 2$:

$4\sqrt{20} = 4 \times 2\sqrt{5} = 8\sqrt{5}$

Therefore, the result is $8\sqrt{5}$.

Among the answer choices, the correct option is:

• e. $8\sqrt{5}$

Would you like to know more about this calculation or any related topics?

Here are five related questions you might find interesting:

1. How do you simplify $\sqrt{50}$?
2. Can you explain how to multiply square roots in general?
3. What are the properties of square roots used in algebra?
4. Could you show how to divide terms under a square root?
5. How would you apply these principles to cube roots?

Tip: When multiplying terms under a square root, combine the terms inside a single square root and simplify if possible.