Question

1. simplify. $sqrt3{2x^2}left(sqrt3{24x^5y^6z^2}divsqrt3{6x^2y^2z}

ight)$
$\bigcirc$ $8xysqrt3{x^2yz}$
$\bigcirc$ $8x^2y^2sqrt3{x^2yz}$
$\bigcirc$ $2x^2y^2sqrt3{x^2yz}$
$\bigcirc$ $2xysqrt3{x^2yz}$

Explanation:

Step1: Simplify the cube root division

$\sqrt[3]{24x^5y^6z^2} \div \sqrt[3]{6x^2y^2z} = \sqrt[3]{\frac{24x^5y^6z^2}{6x^2y^2z}}$

Step2: Compute the fraction inside

$\sqrt[3]{4x^{3}y^{4}z}$

Step3: Split the cube root term

$\sqrt[3]{4x^{3}y^{4}z} = xy\sqrt[3]{4yz}$

Step4: Multiply by the outer term

$\sqrt[3]{2x^2} \times xy\sqrt[3]{4yz} = xy\sqrt[3]{2x^2 \times 4yz}$

Step5: Simplify the product inside

$xy\sqrt[3]{8x^2yz} = xy \times 2\sqrt[3]{x^2yz}$

Step6: Final simplification

$2xy\sqrt[3]{x^2yz}$

Answer:

$2xy\sqrt[3]{x^2yz}$