Question

question 3

simplify the following radical expression.

\\(\sqrt{162}\\)

• \\(9\sqrt{2}\\)
• \\(6\sqrt{4}\\)
• \\(4\sqrt{10}\\)
• cannot be simplified further

Explanation:

Find the largest perfect square factor of 162

$$ 162 = 81 \times 2 $$

Apply the product property of square roots

$$ \sqrt{162} = \sqrt{81 \times 2} = \sqrt{81} \times \sqrt{2} $$

Simplify the perfect square root

$$ \sqrt{81} \times \sqrt{2} = 9\sqrt{2} $$

Answer:

• (A) \(9\sqrt{2}\) (Correct answer)
• (B) \(6\sqrt{4}\)
• (C) \(4\sqrt{10}\)
• (D) Cannot be simplified further