Question

Find the sub-duplicate ratio of

(iii) $169m^6:196n^6$.

Answer 1

Calculation of the sub-duplicate ratio:

For a ratio $x:y$, the corresponding sub-duplicate ratio is $\sqrt{x}:\sqrt{y}$.

The sub-duplicate of the given ratio $169m^6:196n^6$is

$$\begin{gathered} \sqrt{169m^6}:\sqrt{196n^6}=\frac{\sqrt{169m^6}}{\sqrt{196n^6}} \\ =\frac{\sqrt{{\left(13m^3\right)}^2}}{\sqrt{{\left(14n^3\right)}^2}} \\ =\frac{13m^3}{14n^3}(Absorbingthesquarewithsquareroot) \\ =13m^3:14n^3 \end{gathered}$$

Final Answer: Hence, the sub-duplicate ratio of $169m^6:196n^6$ is $13m^3:14n^3$.