Question

√5/3,3/√7 Compare the given pairs of ratio.

Answer 1

$\frac{ \sqrt{5} }{3} = \frac{3}{ \sqrt{7} } \\ \sqrt{5} \times \sqrt{7} = 3 \times 3 \\ \sqrt{35} = 9 \\ \sqrt{35} < 9 \\ \frac{ \sqrt{5} }{3} < \frac{3}{ \sqrt{7} }$
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Answer 2

Answer:

The result is $\begin{aligned}&\frac{\sqrt{2}}{3}<\frac{3}{\sqrt{7}}\end{aligned}$ by comparing the given pairs of ratio.

Step-by-step explanation:

Given: Pairs of ratio$\begin{aligned}&\frac{\sqrt{5}}{3}, \frac{3}{\sqrt{7}} \end{aligned}$.

To Compare: The given pairs of ratio.

Solution:

Pairs of ratio are $\frac{\sqrt{5}}{3}, \frac{3}{\sqrt{7}}$ OR $\sqrt{5}: 3,3: \sqrt{7}$

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

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

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

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

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

Now, Compare both the fractions,

    $\frac{\sqrt{2}}{3}<\frac{3}{\sqrt{7}}$

Hence, The result is $\begin{aligned}&\frac{\sqrt{2}}{3}<\frac{3}{\sqrt{7}}\end{aligned}$ by comparing the given pairs of ratio.