Q. 250 - Intermediate Algebra

Question

In the following exercise , simplify

 $$\begin{gathered} \left(i\right)\frac{\sqrt{196q}}{\sqrt{484q^5}} \\ \left(ii\right)\frac{\sqrt[3]{16m^4}}{\sqrt[3]{54m}} \end{gathered}$$

Step-by-Step Solution

Answer

Part (a) The solution  is $\frac{7}{11q^2}$

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

Step 1. Given information

The given equation are 

$$\begin{gathered} \left(i\right)\frac{\sqrt{196q}}{\sqrt{484q^5}} \\ \left(ii\right)\frac{\sqrt[3]{16m^4}}{\sqrt[3]{54m}} \end{gathered}$$

Step 2. Calculation Part(a)

$$\begin{gathered} \left(i\right)\frac{\sqrt{196q}}{\sqrt{484q^5}}=\frac{\sqrt{196q}}{\sqrt{484q^5}} \mathrm{Write} \mathrm{the} \mathrm{expression} \\ =\frac{\sqrt{196\mathrm{q}}}{\sqrt{484{\mathrm{q}}^5}} \mathrm{Rewrite} \mathrm{using} \mathrm{quotient} \mathrm{property} \\ =\sqrt{\frac{49}{121{\mathrm{q}}^4}} \mathrm{Cancel} \mathrm{out} \mathrm{common} \mathrm{factors} \\ =\frac{7}{11{\mathrm{q}}^2} \mathrm{Simplify} \\ \mathrm{Hence} \mathrm{the} \mathrm{simplified} \mathrm{version} \mathrm{is} \frac{7}{11{\mathrm{q}}^2} \end{gathered}$$

Step 3. Calculation Part(b)

$$\begin{gathered} \left(ii\right)\frac{\sqrt[3]{16m^4}}{\sqrt[3]{54m}}=\frac{\sqrt[3]{16m^4}}{\sqrt[3]{54m}} Write the expression \\ =\sqrt[3]{\frac{16m^4}{54m}} Rewrite u\sin g quotient property \\ =\sqrt[3]{\frac{8m^3}{27}} Cancel out common factor \\ =\frac{2m}{3} \\ Hence the value is \frac{2m}{3}. \end{gathered}$$