Q. 65 - Intermediate Algebra

Question

In the following exercises, use the Product Property to simplify radical expressions a $\sqrt[5]{64}$, b.$\sqrt[3]{256}$

Step-by-Step Solution

Answer

The expression in simplified form is $2\sqrt[5]{2},4\sqrt[3]{4}$ respectively

Step 1: Given information

Given the expression $\sqrt[5]{64}$,$\sqrt[3]{256}$

Step 2: Using the product property to simplify

Using the property, we get

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

Step 3: Checking for another expression

Using the property, we get

$$\begin{gathered} \sqrt[3]{256}=\sqrt[3]{64·4} \\ \sqrt[3]{256}=4·\sqrt[3]{4} \\ \sqrt[3]{256}=4\sqrt[3]{4} \end{gathered}$$