Q. 8.7TI - Intermediate Algebra

Question

Simplify: $\left(a\right) \sqrt[3]{-27} \left(b\right) \sqrt[4]{-256} \left(c\right)\sqrt[5]{-32}$

Step-by-Step Solution

Answer

The solutions of (a) is $-3$, (b) is there is no real number and (c) is $-2$

Part (a). Step 1. Given information

The root: $\sqrt[3]{-27}$

Part (a) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[3]{-27} \\ =-3 \end{gathered}$$

Since, ${(-3)}^3=-27$

Therefore, the solution is $-3$

Part (b). Step 1. Given information

The root: $\sqrt[4]{-256}$

Part (b) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[4]{-256} \\ Not a real number \end{gathered}$$

No real number raised to the fourth power is negative.

Part (c). Step 1. Given information

The root: $\sqrt[5]{-32}$

Part (c) Step 2. Calculation

We have,

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

Since, ${(-2)}^5=-32$

Therefore, the solution is $-2$