Question

what is the following sum?

(4sqrt{5} + 2sqrt{5})

• (8sqrt{10})
• (6sqrt{10})
• (8sqrt{5})
• (6sqrt{5})

Explanation:

Identify like radicals

$$ 4\sqrt{5} \text{ and } 2\sqrt{5} \text{ share the common radical factor } \sqrt{5} $$

Combine coefficients

$$ 4\sqrt{5} + 2\sqrt{5} = (4 + 2)\sqrt{5} = 6\sqrt{5} $$

Answer:

• \(8\sqrt{10}\)
• \(6\sqrt{10}\)
• \(8\sqrt{5}\)
• \(6\sqrt{5}\) (Correct answer)