Q. 63 - Intermediate Algebra

Question

In the following exercises, use the Product Property to simplify radical expressions a. $\sqrt[4]{32}$,b. $\sqrt[5]{64}$

Step-by-Step Solution

Answer

The expression in simplified form is $2\sqrt[4]{2},2\sqrt[5]{2}$ respectively

Step 1: Given information

Given the expression $\sqrt[4]{32},\sqrt[5]{64}$

Step 2: Using the product property to simplify

Using the property, we get

$$\begin{gathered} \sqrt[4]{32}=\sqrt[4]{16·2} \\ \sqrt[4]{32}==2·\sqrt[4]{2} \\ \sqrt[4]{32}==2\sqrt[4]{2} \end{gathered}$$

Step 3: Simplifying for another expression

Using the property, we get

$$\begin{gathered} \sqrt[5]{64}=\sqrt[5]{32·2} \\ \sqrt[5]{64}=2·\sqrt[5]{2} \\ \sqrt[5]{64}=2\sqrt[5]{2} \end{gathered}$$