Q. 247 - Intermediate Algebra

Question

In the following exercise simplify

$$\begin{gathered} \left(i\right)\frac{\sqrt{200m^5}}{\sqrt{98m}} \\ \left(ii\right)\frac{\sqrt[3]{54y^2}}{\sqrt[3]{2y^5}} \end{gathered}$$

Step-by-Step Solution

Answer

Part (a) The solution  is $\frac{10m^2}{7}$

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

Step 1. Given information

The given equations are 

$$\begin{gathered} \left(i\right)\frac{\sqrt{200m^5}}{\sqrt{98m}} \\ \left(ii\right)\frac{\sqrt[3]{54y^2}}{\sqrt[3]{2y^5}} \end{gathered}$$

Step 2. Calculation Part(a)

$$\begin{gathered} \left(i\right)\frac{\sqrt{200m^5}}{\sqrt{98m}}=\frac{\sqrt{200m^5}}{\sqrt{98m}} \mathrm{Write} \mathrm{the} \mathrm{expression} \\ =\sqrt{\frac{200m^5}{98m}}\mathrm{Rewrite} \mathrm{using} \mathrm{quotient} \mathrm{property} \\ =\sqrt{\frac{100m^4}{49}} \mathrm{Cancel} \mathrm{out} \mathrm{the} \mathrm{common} \mathrm{factors} \\ =\frac{10m^2}{7}\mathrm{Simplify} \\ \mathrm{Hence} \mathrm{the} \mathrm{simplified} \mathrm{value} \mathrm{is} \frac{10m^2}{7} \end{gathered}$$

Step 3. Calculation Part(b)

$$\begin{gathered} \left(ii\right)\frac{\sqrt[3]{54y^2}}{\sqrt[3]{2y^5}}=\frac{\sqrt[3]{54y^2}}{\sqrt[3]{2y^5}}\mathrm{Write} \mathrm{the} \mathrm{expressio}n \\ =\sqrt[3]{\frac{54y^2}{2y^5}} \mathrm{Rewrite} \mathrm{using} \mathrm{quotient} \mathrm{property} \\ =\sqrt[3]{\frac{27}{y^3}} \mathrm{Cancel} \mathrm{out} \mathrm{common} \mathrm{factors} \\ =\frac{3}{y} \\ \mathrm{Hence} \mathrm{the} \mathrm{simplified} \mathrm{value} \mathrm{is} \frac{3}{y} \end{gathered}$$