Question

find the simplified product:
\\(\sqrt{2x^3} \cdot \sqrt{18x^5}\\)

\\(\sqrt{6x^4}\\)

\\(\sqrt{36x^8}\\)

\\(18x^4\\)

\\(6x^4\\)

Explanation:

Multiply the radicands

Using the Product Property of Radicals knowledge point

$$ \sqrt{2x^3} \cdot \sqrt{18x^5} = \sqrt{2x^3 \cdot 18x^5} $$

Simplify the expression inside the radical

Using the Simplifying Radical Products knowledge point

$$ \sqrt{36x^8} $$

Take the square root

Using the Simplifying Radical Products knowledge point

$$ \sqrt{36} \cdot \sqrt{x^8} = 6x^4 $$

Answer:

• (A) \(\sqrt{6x^4}\)
• (B) \(\sqrt{36x^8}\)

<mcq-option>(C) \(18x^4\)</mcq-correct>

• (D) \(6x^4\) (Correct answer)