Question

Find the sub-duplicate ratio of

(i) $49:81$.

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 4:9 is calculated as,

$$\begin{gathered} \sqrt{49}:\sqrt{81}=\frac{\sqrt{49}}{\sqrt{81}} \\ =\frac{\sqrt{7^2}}{\sqrt{9^2}} \\ =\frac{7}{9}(Absorbingthesquarewithsquareroot) \\ =7:9 \end{gathered}$$

Final Answer: Hence, the sub-duplicate ratio of $49:81$ is $7:9$.