Question

practice probler which expression is equivalent to \\(sqrt3{48x^9y^5}\\) multiple choice a \\(2x^3ysqrt3{6y^2}\\) b \\(8x^3ysqrt3{6y^2}\\) c \\(6x^3ysqrt3{8y^2}\\) d \\(2x^3ysqrt3{6xy^2}\\)

Explanation:

Step1: Factor radicand into cubes

$\sqrt[3]{48x^9y^5} = \sqrt[3]{8 \cdot 6 \cdot x^9 \cdot y^3 \cdot y^2}$

Step2: Separate perfect cube factors

$\sqrt[3]{8} \cdot \sqrt[3]{x^9} \cdot \sqrt[3]{y^3} \cdot \sqrt[3]{6y^2}$

Step3: Simplify perfect cube roots

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

Step4: Combine simplified terms

$2x^3y\sqrt[3]{6y^2}$

Answer:

A. $2 x^3 y \sqrt[3]{6y^2}$