Question

1. simplify $sqrt3{125x^{3}y^{4}z}$.

$\bigcirc$ $125sqrt3{yz}$
$\bigcirc$ $5x^{3}y^{3}sqrt3{yz}$
$\bigcirc$ $125xysqrt3{yz}$
$\bigcirc$ $5xysqrt3{yz}$

Explanation:

Step1: Factor terms inside cube root

$\sqrt[3]{125x^3y^4z} = \sqrt[3]{125 \cdot x^3 \cdot y^3 \cdot y \cdot z}$

Step2: Separate perfect cube factors

$\sqrt[3]{125} \cdot \sqrt[3]{x^3} \cdot \sqrt[3]{y^3} \cdot \sqrt[3]{yz}$

Step3: Simplify perfect cube roots

$5 \cdot x \cdot y \cdot \sqrt[3]{yz}$

Step4: Combine simplified terms

$5xy\sqrt[3]{yz}$

Answer:

D. $5xy\sqrt[3]{yz}$