Question

Find the sub-duplicate ratio of

(ii) $16x^4:25y^4$.

Answer 1

Calculation of the sub-duplicate:

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

The sub-duplicate of the given ratio is

$$\begin{gathered} \sqrt{16x^4}:\sqrt{25y^4}=\frac{\sqrt{16x^4}}{\sqrt{25y^4}} \\ =\frac{\sqrt{{\left(4x^2\right)}^2}}{\sqrt{{\left(5y^2\right)}^2}} \\ =\frac{4x^2}{5y^2}(Removingthesquareroot) \\ =4x^2:5y^2 \end{gathered}$$

Final Answer: The sub-duplicate ratio of $16x^4:25y^4$ is $4x^2:5y^2$.