Chapter A.10, Problem 38AYU

To determine

To find: Simplify the expression $\sqrt[4]{32x}+\sqrt[4]{2x^5}$.

Answer to Problem 38AYU

The value of $\sqrt[4]{32x}+\sqrt[4]{2x^5}=\sqrt[4]{2x}\left(2-x\right)$.

Explanation of Solution

Given:

It is asked to find the simplest form of the given expression $\sqrt[4]{32x}+\sqrt[4]{2x^5}$.

Calculation:

Consider $\sqrt[4]{32x}+\sqrt[4]{2x^5}$,

$\sqrt[4]{32x}+\sqrt[4]{2x^5}=\sqrt[4]{16\times 2\times x}-\sqrt[4]{2x\times x^4}$

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

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

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