Q. 67 - Intermediate Algebra

Question

In the following exercises, simplify using absolute value signs as needed.

 $$\begin{gathered} \sqrt{y^{11}} \\ \sqrt[3]{r^5} \\ \sqrt[4]{s^{10}} \end{gathered}$$

Step-by-Step Solution

Answer

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

Step 1: Given information

Given the expression $\sqrt{y^{11}},\sqrt[3]{r^5},\sqrt[4]{s^{10}}$

Step 2: Using the product property and simplifying

Using the property, we get

$$\begin{gathered} \sqrt{y^{11}}=\sqrt{y^{10}y} \\ \sqrt{y^{11}}=\sqrt{y^{10}}\sqrt{y} \\ \sqrt{y^{11}}==y^5\sqrt{y} \end{gathered}$$

Step 3: Simplify another expression

Simplifying, we get

$$\begin{gathered} \sqrt[3]{r^5}=\sqrt[3]{r^3{r}^2} \\ \sqrt[3]{r^5}=\sqrt[3]{r^3}\sqrt[3]{r^2} \\ \sqrt[3]{r^5}=r\sqrt[3]{r^2} \end{gathered}$$

Step 4: Simplifying another expression

Using the property, we get

$$\begin{gathered} \sqrt[4]{s^{10}}=\sqrt[4]{s^8{s}^2} \\ \sqrt[4]{s^{10}}=\sqrt[4]{s^8}\sqrt[4]{s^2} \\ \sqrt[4]{s^{10}}==s\sqrt[2]{s^2} \end{gathered}$$