Question

Compare the following pair of ratio.
$\frac{\sqrt{5}}{3},\frac{3}{\sqrt{7}}$

Answer 1

$\frac{\sqrt{5}}{3},\frac{3}{\sqrt{7}}$

$\sqrt{5}:3,3:\sqrt{7}$

$\frac{\sqrt{5}}{3},\frac{3}{\sqrt{7}},$

LCM of $3,\sqrt{7},$ is $3\sqrt{7}$

$\therefore \frac{\sqrt{5}}{3}\times \frac{\sqrt{7}}{\sqrt{7}}=\frac{\sqrt{35}}{3\sqrt{7}}$

$\frac{3}{\sqrt{7}}\times \frac{3}{3}=\frac{9}{3\sqrt{7}}$

$\frac{\sqrt{35}}{3\sqrt{7}},\frac{9}{3\sqrt{3}}$

clearly, $\sqrt{35}<9$

$\therefore \frac{\sqrt{35}}{3\sqrt{7}}<\frac{9}{3\sqrt{7}}$

$\Rightarrow \frac{\sqrt{5}}{3}<\frac{3}{\sqrt{7}}$