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Question

Compare the following pair of ratios:
$$\frac{\sqrt{5}}{3},\frac{3}{\sqrt{7}}$$

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Solution

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$$\sqrt{5}\sqrt{7}=\sqrt{57}=\sqrt{35}$$
$$3*3=9=\sqrt{81}$$
Now, $$\sqrt{35}<\sqrt{81}$$
$$\therefore \frac{\sqrt{5}}{3}<\frac{3}{\sqrt{7}}$$

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