Question

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

Short answer

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

Step-by-step solution

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,

$$\begin{gathered} \sqrt[4]{-256} \\ Notarealnumber \end{gathered}$$

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$-2$