Q. 66 - Intermediate Algebra

Question

In the following exercises, use the Product Property to simplify radical expressions a $\sqrt[4]{3125}$, b. $\sqrt[3]{81}$

Step-by-Step Solution

Answer

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

Step 1: Given information

Given the expression $\sqrt[4]{3125},\sqrt[3]{81}$

Step 2: Using the product property to simplify

Using the property, we get

$$\begin{gathered} \sqrt[4]{3125}=\sqrt[4]{625·5} \\ \sqrt[4]{3125}=\sqrt[4]{625}\times \sqrt[4]{5} \\ \sqrt[4]{3125}=\sqrt[4]{5^4}\times \sqrt[4]{5} \\ \sqrt[4]{3125}=5\sqrt[4]{5} \end{gathered}$$

Step 3: Simplifying for another expression 81 3 = 27 · 3 3 81 3 = 27 3 × 3 3 81 3 = 3 3 3 × 3 3 81 3 = 3 3 3

Simplifying, we get