Q. 248 - Intermediate Algebra

Question

In the following exercise simplify.

$$\begin{gathered} \left(i\right)\frac{\sqrt{108n^7}}{\sqrt{243n^3}} \\ \left(ii\right)\frac{\sqrt[3]{54y}}{\sqrt[3]{16y^4}} \end{gathered}$$

Step-by-Step Solution

Answer

Part (a) The solution  is $\frac{2n^3}{3}$

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

Step 1. Given information

The given equations are $$\begin{gathered} \left(i\right)\frac{\sqrt{108n^7}}{\sqrt{243n^3}} \\ \left(ii\right)\frac{\sqrt[3]{54y}}{\sqrt[3]{16y^4}} \end{gathered}$$

Step 2. Calculation Part(a)

$$\begin{gathered} \left(i\right)\frac{\sqrt{108n^7}}{\sqrt{243n^3}}=\frac{\sqrt{108n^7}}{\sqrt{243n^3}} \mathrm{Write} \mathrm{the} \mathrm{expression} \\ =\sqrt[]{\frac{108{\mathrm{n}}^7}{243{\mathrm{n}}^2}} \mathrm{Rewrite} \mathrm{using} \mathrm{quotient} \mathrm{property} \\ =\sqrt[]{\frac{4n^4}{9} }C\mathrm{ancel} \mathrm{out} \mathrm{common} \mathrm{factor} \\ =\frac{2n^2}{3} \\ \mathrm{Hnece} \mathrm{the} \mathrm{simplified} \mathrm{value} \mathrm{i}s \frac{2n^2}{3} \end{gathered}$$

Step 3. Calculation Part(b)

$$\begin{gathered} \left(ii\right)\frac{\sqrt[3]{54y}}{\sqrt[3]{16y^4}}=\frac{\sqrt[3]{54y}}{\sqrt[3]{16y^4}} \mathrm{Write} \mathrm{the} \mathrm{expression} \\ =\sqrt[3]{\frac{54y}{16y^4}} \mathrm{Rewrite} \mathrm{using} \mathrm{quotient} \mathrm{property} \\ =\sqrt[3]{\frac{27}{8y^3} } \mathrm{Cancel} \mathrm{out} \mathrm{the} \mathrm{common} \mathrm{property} \\ =\frac{3}{2y} \\ \mathrm{Hence} \mathrm{the} \mathrm{simplified} \mathrm{value} \mathrm{is} \frac{3}{2y} \end{gathered}$$