Simplify the following.
$\left(2\sqrt{5}\right)\left(4\sqrt{7}\right)$

• A. $8\sqrt{2}$
• B. $8\sqrt{13}$
• C. $6\sqrt{35}$
• D. $8\(\sqrt{35}\)$

Answer: (D)

Verified step by step guidance

1. Start with the expression \(\left(2\sqrt{5}\right)\left(4\sqrt{7}\right)\) and recognize that you can multiply the coefficients (numbers outside the square roots) together and the radicands (numbers inside the square roots) together separately.
2. Multiply the coefficients: \(2 \times 4 = 8\).
3. Multiply the radicands inside the square roots: \(\sqrt{5} \times \sqrt{7} = \sqrt{5 \times 7} = \sqrt{35}\).
4. Combine the results from the previous steps to write the product as \(8\sqrt{35}\).
5. Since \(\sqrt{35}\) cannot be simplified further (35 has no perfect square factors other than 1), the expression is simplified as \(8\sqrt{35}\).