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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.

Learn how to simplify 4√10 × √2 step by step by using the properties of square roots and radicals. Suitable for students in Grades 9-10, this problem involves key algebraic concepts like multiplying and simplifying square roots.

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