Q. 8.5TI - Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

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

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 $3$