Question

What is the simplified form of the following expression 7(^3√2x)-3(^3√16x)-3(^3√8x)

Answer 1

Given expression: $7\sqrt[3]{2x}-3\sqrt[3]{16x}-3\sqrt[3]{8x}$

$7\sqrt[3]{2x}=7\sqrt[3]{2}\sqrt[3]{x}$

$3\sqrt[3]{16x}=6\sqrt[3]{2}\sqrt[3]{x}$

$3\sqrt[3]{8x}=6\sqrt[3]{x}$

$=7\sqrt[3]{2}\sqrt[3]{x}-6\sqrt[3]{2}\sqrt[3]{x}-6\sqrt[3]{x}$

$=7\sqrt[3]{2x}-6\sqrt[3]{2x}-6\sqrt[3]{x}$

$\mathrm{Add\:similar\:elements:}$

$=\sqrt[3]{2x}-6\sqrt[3]{x}$

Therefore, correct option is C) $\sqrt[3]{2x}-6\sqrt[3]{x}$.