The sub-duplicate ratio of $9 a^{2} b^{2} : 16 r^{2} s^{2}$ is _____

3 a : 4 r

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4 a b : 3 r s

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3 a b : 4 r s

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3 b : 4 s

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Solution

The correct option is C $3 a b : 4 r s$
The sub-duplicate ratio of $x : y$ is $\sqrt{x} : \sqrt{y}$
$∴$ The subduplicate ratio of $9 a^{2} b^{2} : 16 r^{2} s^{2}$ is $\sqrt{9 a^{2} b^{2}} : \sqrt{16 r^{2} s^{2}}$
$= 3 a b : 4 r s$

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