Q. 221 - Intermediate Algebra

Question

Simplify:

$\frac{1}{2}\sqrt[4]{80}-\frac{2}{3}\sqrt[4]{405}$

Step-by-Step Solution

Answer

The value of the given expression is $-\sqrt[4]{5}.$

Step 1. Given Information

The given expression is

 $\frac{1}{2}\sqrt[4]{80}-\frac{2}{3}\sqrt[4]{405}.$

Step 2. Simplify the radicals

Like radicals can be added or subtracted so,

$$\begin{gathered} \frac{1}{2}\sqrt[4]{80}-\frac{2}{3}\sqrt[4]{405} \\ =\frac{1}{2}\sqrt[4]{16·5}-\frac{2}{3}\sqrt[4]{81·5} \\ =\frac{1}{2}·\sqrt[4]{{\left(2\right)}^4}·\sqrt[4]{5}-\frac{2}{3}·\sqrt[4]{{\left(3\right)}^4}·\sqrt[4]{5} \\ =\frac{1}{2}·2·\sqrt[4]{5}-\frac{2}{3}·3·\sqrt[4]{5} \\ =\sqrt[4]{5}-2\sqrt[4]{5} \\ =-\sqrt[4]{5} \end{gathered}$$