Q. 8.8TI - Intermediate Algebra

Question

Simplify: $\left(a\right)\sqrt[3]{-216} \left(b\right)\sqrt[4]{-81} \left(c\right)\sqrt[5]{1024}$

Step-by-Step Solution

Answer

The solutions of (a) is $-6$, (b) is no real number and (c) is $-4$

Part (a). Step 1. Given information

The root: $\sqrt[3]{-216}$

Part (a) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[3]{-216} \\ =-6 \end{gathered}$$

Since, $-6^3=-216$

Therefore, the solution is $-6$

Part (b). Step 1. Given information

The root: $\sqrt[4]{-81}$

Part (b) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[4]{-81} \\ Not a real number \end{gathered}$$

No real number is raised to the fourth power is negative.

Part (c). Step 1. Given information

The root: $\sqrt[5]{-1024}$

Part (c) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[5]{-1024} \\ =-4 \end{gathered}$$

Since, ${(-4)}^5=-1024$

Therefore, the solution is $-4$