Question

simplify: \\(\sqrt{18x^7}\\)

\\(9x^3\sqrt{x}\\)

\\(3x^3\sqrt{2x}\\)

\\(3x\sqrt{x^3}\\)

Explanation:

Factor the radicand into perfect squares

Using the Product Property of Radicals and Radical Simplification knowledge points

$$ 18x^7 = (9 \cdot 2) \cdot (x^6 \cdot x) = (9x^6) \cdot (2x) $$

Apply the product property of radicals

Using the Product Property of Radicals and Radical Simplification knowledge points

$$ \sqrt{18x^7} = \sqrt{9x^6 \cdot 2x} = \sqrt{9x^6} \cdot \sqrt{2x} $$

Simplify the perfect square radical

Using the Radical Simplification knowledge point

$$ \sqrt{9x^6} \cdot \sqrt{2x} = 3x^3\sqrt{2x} $$

Answer:

• (A) \(9x^3\sqrt{x}\)
• (B) \(3x^3\sqrt{2x}\) (Correct answer)
• (C) \(3x\sqrt{x^3}\)