Q. 8.6TI - Intermediate Algebra

Question

Simplify: $\left(a\right) \sqrt[3]{1000} \left(b\right) \sqrt[4]{16} \left(c\right) \sqrt[5]{243}$

Step-by-Step Solution

Answer

The solution of (a), (b) and (c) are $10, 2 and 3$ respectively.

Part (a). Step 1. Given information

The root: $\sqrt[3]{1000}$

Part (a) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[3]{1000} \\ =10 \end{gathered}$$

Since, ${10}^3=1000$

Therefore, the solution is $10$

Part (b). Step 1. Given information

The root: $\sqrt[4]{16}$

Part (b) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt[4]{16} \\ =2 \end{gathered}$$

Since, ${\left(2\right)}^4=16$

Therefore, the solution is $2$

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 $3$