Chapter A.10, Problem 37AYU

To determine

To find: Simplify the expression $\sqrt[3]{16x^4}-\sqrt[3]{2x}$.

Answer to Problem 37AYU

The value of $\sqrt[3]{16x^4}-\sqrt[3]{2x}=\sqrt[3]{2x}\left(2x-1\right)$.

Explanation of Solution

Given:

It is asked to find the simplest form of the given expression $\sqrt[3]{16x^4}-\sqrt[3]{2x}$.

Calculation:

Consider $\sqrt[3]{16x^4}-\sqrt[3]{2x}$,

$\sqrt[3]{16x^4}-\sqrt[3]{2x}=\sqrt[3]{8\times 2\times x^3\times x}-\sqrt[3]{2x}$

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

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

$=\sqrt[3]{2x}\left(2x-1\right)$