Question

subtract. assume that all variables represent positive real numbers.
\sqrt3{24x} - \sqrt3{192x}
\sqrt3{24x} - \sqrt3{192x} = \square
(type an exact answer, using radicals as needed. simplify your answer.)

Explanation:

Step1: Factor radicands for cubes

$\sqrt[3]{24x} = \sqrt[3]{8 \cdot 3x}$, $\sqrt[3]{192x} = \sqrt[3]{64 \cdot 3x}$

Step2: Simplify perfect cube roots

$\sqrt[3]{8 \cdot 3x} = 2\sqrt[3]{3x}$, $\sqrt[3]{64 \cdot 3x} = 4\sqrt[3]{3x}$

Step3: Subtract like radicals

$2\sqrt[3]{3x} - 4\sqrt[3]{3x} = (2-4)\sqrt[3]{3x}$

Answer:

$-2\sqrt[3]{3x}$