Question

simplify \\(3\sqrt{150}\\) as much as possible.

• 18
• \\(5\sqrt{6}\\)
• \\(15\sqrt{6}\\)
• \\(18\sqrt{25}\\)

Explanation:

Factor the radicand to find perfect squares

$$ 150 = 25 \times 6 = 5^2 \times 6 $$

Apply the product property of square roots

$$ 3\sqrt{150} = 3\sqrt{25 \times 6} = 3 \times \sqrt{25} \times \sqrt{6} $$

Simplify the expression

$$ 3 \times 5 \times \sqrt{6} = 15\sqrt{6} $$

Answer:

• 18
• \(5\sqrt{6}\)
• \(15\sqrt{6}\) (Correct answer)
• \(18\sqrt{25}\)