Q. 15 - Intermediate Algebra

Question

In the following exercises, simplify. 

$\left(a\right)\sqrt[3]{-8}\left(b\right)\sqrt[4]{-81}\left(c\right)\sqrt[5]{-32}$

Step-by-Step Solution

Answer

Hence,

$\begin{array}{l}\left(a\right)\sqrt[3]{-8}=-3\\ \left(b\right)\sqrt[4]{-81}=\text{No real number }\\ \left(c\right)\sqrt[5]{-32}=-2\end{array}$

Step 1. Given information

$\begin{array}{l}\text{The given expressions are}\\ \left(a\right)\sqrt[3]{-8}\left(b\right)\sqrt[4]{-81}\left(c\right)\sqrt[5]{-32}\\ \text{We have to simplify the given expressions}\end{array}$

Step 2. Simplify the expression in part (a)

$\begin{array}{l}\Rightarrow \sqrt[3]{-8}=\sqrt[3]{{\left(-2\right)}^3}\left[\because {\left(-2\right)}^3=-8\right]\\ =-2\end{array}$

Step 3. Simplify the expression in part (b)

$\begin{array}{l}\Rightarrow \sqrt[4]{-81}\\ \left[\because {\left(-3\right)}^4=81\right]\\ \text{Therefore, no real number}\end{array}$

Step 4. Simplify the expression in part (c)

$\begin{array}{l}\Rightarrow \sqrt[5]{-32}=\sqrt[5]{{\left(-2\right)}^5}\left[\because {\left(-2\right)}^5=-32\right]\\ =-2\end{array}$