Question

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

\\(\sqrt{6x^4}\\)
\\(\sqrt{36x^8}\\)
\\(18x^4\\)
\\(6x^4\\)

find the simplified product:
\\(\sqrt3{9x^4} \cdot \sqrt3{3x^8}\\)

\\(\sqrt3{12x^{12}}\\)
\\(\sqrt3{27x^{12}}\\)
\\(3x^4\\)
\\(9x^6\\)

Explanation:

Multiply the expressions under the radical

Using the Product Property of Radicals knowledge point

$$ \sqrt{2x^3} \cdot \sqrt{18x^5} = \sqrt{2x^3 \cdot 18x^5} = \sqrt{36x^8} $$

Simplify the resulting square root

Using the Simplifying Radical Products knowledge point

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

Multiply the expressions under the cube radical

Using the Product Property of Radicals knowledge point

$$ \sqrt[3]{9x^4} \cdot \sqrt[3]{3x^8} = \sqrt[3]{9x^4 \cdot 3x^8} = \sqrt[3]{27x^{12}} $$

Simplify the resulting cube root

Using the Simplifying Radical Products knowledge point

$$ \sqrt[3]{27x^{12}} = \sqrt[3]{27} \cdot \sqrt[3]{x^{12}} = 3x^4 $$

Answer:

Question 1

• (A) \(\sqrt{6x^4}\)
• (B) \(\sqrt{36x^8}\)
• (C) \(18x^4\)
• (D) \(6x^4\) (Correct answer)

Question 2

• (A) \(\sqrt[3]{12x^{12}}\)
• (B) \(\sqrt[3]{27x^{12}}\)
• (C) \(3x^4\) (Correct answer)
• (D) \(9x^6\)