Q. 8.102 - Intermediate Algebra

Question

In the following exercise ,simplify 

$$\begin{gathered} \left(a\right) \frac{1}{\sqrt[3]{2}} \\ \left(b\right) \sqrt[3]{\frac{3}{20}} \\ \left(c\right) \frac{2}{\sqrt[3]{25n}} \end{gathered}$$

Step-by-Step Solution

Answer

$$\begin{gathered} \left(a\right) \frac{\sqrt[3]{4}}{2} \\ \left(b\right) \frac{\sqrt[3]{3}.\sqrt[3]{{20}^2}}{20} \\ \left(c\right) \frac{2\sqrt[3]{{25}^2{n}^2}}{25n} \end{gathered}$$ 

Part (a) Step 1. Given information.

Given expression:

$\frac{1}{\sqrt[3]{2}}$

Part (a) Step 2. Finding solution.

Finding the solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\sqrt[3]{2^2}$.

$$\begin{gathered} \frac{1}{\sqrt[3]{2}}\times \frac{\sqrt[3]{2^2}}{\sqrt[3]{2^2}} \\ =\frac{\sqrt[4]{2^2}}{2} \end{gathered}$$

Part (b) Step 1. Given information.

Given expression:

$\sqrt[3]{\frac{3}{20}}$

Part (b) Step 2. Finding the solution.

Finding the solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\sqrt[3]{{20}^2}$.

$$\begin{gathered} \frac{\sqrt[3]{3}}{\sqrt[3]{20}}\times \frac{\sqrt[3]{{20}^2}}{\sqrt[3]{{20}^2}} \\ =\frac{\sqrt[3]{3}.\sqrt[3]{{20}^2}}{20} \end{gathered}$$

Part (c) Step 1. Given information.

Given expression :

$\frac{2}{\sqrt[3]{25n}}$

Part (c) Step 2. Finding the solution.

Finding the solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\sqrt[3]{{25}^2{n}^2}$.

$$\begin{gathered} \frac{2}{\sqrt[3]{25n}}\times \frac{\sqrt[3]{{25}^2{n}^2}}{\sqrt[3]{{25}^2{n}^2}} \\ =\frac{2\sqrt[3]{{25}^2{n}^2}}{25n} \end{gathered}$$