Q. 245 - Intermediate Algebra

Question

In the following exercise , simplify  

$$\begin{gathered} \left(i\right)\frac{\sqrt{128}}{\sqrt{72}} \\ \left(ii\right)\frac{\sqrt[3]{128}}{\sqrt[3]{54}} \end{gathered}$$

Step-by-Step Solution

Answer

Part (a) The solution  is $\frac{4}{3}$.

Part (b) The solution  is $\frac{4}{3}$.

Step 1. Given information

The given equation are $$\begin{gathered} \left(i\right)\frac{\sqrt{128}}{\sqrt{72}} \\ \left(ii\right)\frac{\sqrt[3]{128}}{\sqrt[3]{54}} \end{gathered}$$

Step 2. Calculation Part(a)

$$\begin{gathered} \left(i\right)\frac{\sqrt{128}}{\sqrt{72}}=\frac{\sqrt{128}}{\sqrt{72}} \mathrm{Write} \mathrm{the} \mathrm{expression} \\ =\sqrt{\frac{128}{72}} \mathrm{Rewrite} \mathrm{using} \mathrm{quotient} \mathrm{property} \\ =\sqrt{\frac{16}{9}} \\ =\frac{4}{3} \\ \mathrm{Hnece} \mathrm{the} \mathrm{simplified} \mathrm{value} \mathrm{is} \frac{4}{3} \end{gathered}$$

Step 3. Calculation Part(b)

$$\begin{gathered} \left(ii\right)\frac{\sqrt[3]{128}}{\sqrt[3]{54}}=\frac{\sqrt[3]{128}}{\sqrt[3]{54}} \mathrm{Write} \mathrm{the} \mathrm{expression} \\ =\sqrt[3]{\frac{128}{54}} \mathrm{Rewrite} \mathrm{using} \mathrm{quotient} \mathrm{property} \\ =\sqrt[3]{\frac{64}{27}} \\ =\frac{4}{3} \\ \mathrm{Hence} \mathrm{the} \mathrm{simplified} \mathrm{value} \mathrm{is} \frac{4}{3}. \end{gathered}$$