Question

Simplify:$\left(a\right)\sqrt[3]{27}\left(b\right)\sqrt[4]{256}\left(c\right)\sqrt[5]{243}$

Short answer

The solutions of (a), (b) and (c) are$3,4and3$respectively.

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,

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

Since, ${\left(4\right)}^4=256$

Therefore, the solution is$4$

Part (c). Step 1. Given information

The root:$\sqrt[5]{243}$

Part (c) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[5]{243} \\ =3 \end{gathered}$$

Since, ${\left(3\right)}^5=243$

Therefore, the solution is$3$