Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$$\sqrt [ 3 ] { x } \left( \sqrt [ 3 ] { x ^ { 2 } } - \sqrt [ 3 ] { 24 x ^ { 2 } } \right)$$
A) $x - 2 x \sqrt [ 3 ] { 3 }$
B) $x - 8 x \sqrt [ 3 ] { 3 }$
C) $x - 2 x ^ { 3 } \sqrt [ 3 ] { 3 }$
D) $x - 6 x$

Question

Quizplus · Accepted Answer

To solve the given expression, we distribute $\sqrt[3]{x}$ across the terms inside the parenthesis: $\sqrt[3]{x}(\sqrt[3]{x^2} - \sqrt[3]{24x^2})$. This simplifies to $\sqrt[3]{x^3} - \sqrt[3]{24x^3}$. Since $\sqrt[3]{x^3} = x$ and $\sqrt[3]{24x^3} = 2x\sqrt[3]{3}$, the expression simplifies to $x - 2x\sqrt[3]{3}$, which matches choice A.

Choose the One Alternative That Best Completes the Statement or Answers