Q. 246 - Intermediate Algebra

Question

In the following exercise simplify

$$\begin{gathered} \left(i\right)\frac{\sqrt{48}}{\sqrt{75}} \\ \left(ii\right)\frac{\sqrt[3]{81}}{\sqrt[3]{24}} \end{gathered}$$

Step-by-Step Solution

Answer

Part (a) The solution  is $\frac{4}{5}$.

Part (b) The solution  is $\frac{3}{2}$.

Step 1. Given information

The given equation are 

$$\begin{gathered} \left(i\right)\frac{\sqrt{48}}{\sqrt{75}} \\ \left(ii\right)\frac{\sqrt[3]{81}}{\sqrt[3]{24}} \end{gathered}$$

Step 2. Calculation Part(a)

$$\begin{gathered} \left(i\right)\frac{\sqrt{48}}{\sqrt{75}}=\frac{\sqrt{48}}{\sqrt{75}} \mathrm{Write} \mathrm{the} \mathrm{expression} \\ =\sqrt{\frac{48}{75}} \mathrm{Rewite} \mathrm{using} \mathrm{quotient} \mathrm{property} \\ =\sqrt{\frac{16}{25}} \\ =\frac{4}{5} \\ \mathrm{Hence} \mathrm{the} \mathrm{simplified} \mathrm{value} \mathrm{is} \frac{4}{5} \end{gathered}$$

Step 3. Calculation Part (b)

$$\begin{gathered} \frac{\sqrt[3]{81}}{\sqrt[3]{24}}=\frac{\sqrt[3]{81}}{\sqrt[3]{24}} \mathrm{Write} \mathrm{the} \mathrm{expression} \\ = \sqrt[3]{\frac{81}{24}} \mathrm{Rewrite} \mathrm{using} \mathrm{quotient} \mathrm{property} \\ =\sqrt[3]{\frac{27}{8}} \\ =\frac{3}{2} \\ \mathrm{Hence} \mathrm{simplified} \mathrm{value} \mathrm{is} \frac{3}{2} \end{gathered}$$