Question

select the correct answer.

which expression is equivalent to \\(\sqrt3{56x^7y^5}\\) if \\(x \
eq 0\\) and \\(y \
eq 0\\)?

\\(2x^2y\sqrt3{7xy^2}\\)

\\(8xy\sqrt3{7x^4y^2}\\)

\\(8x^2y\sqrt3{7xy^2}\\)

\\(2x^4y^2\sqrt3{7}\\)

Explanation:

Factor the terms inside the cube root into perfect cubes

$$
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$$

Group perfect cubes and remaining factors

$$ \sqrt[3]{56x^7y^5} = \sqrt[3]{(2^3 \cdot x^6 \cdot y^3) \cdot (7 \cdot x \cdot y^2)} $$

Simplify the radical expression

$$ \sqrt[3]{2^3 \cdot x^6 \cdot y^3} \cdot \sqrt[3]{7xy^2} = 2x^2y\sqrt[3]{7xy^2} $$

Answer:

• (A) \(2x^2y\sqrt[3]{7xy^2}\) (Correct answer)
• (B) \(8xy\sqrt[3]{7x^4y^2}\)
• (C) \(8x^2y\sqrt[3]{7xy^2}\)
• (D) \(2x^4y^2\sqrt[3]{7}\)