Question

Compare the following pairs of
pairs. Of ratios
√5÷3,3÷√7

​

Answer 1

We have,

• To compare two fractions.

Given,

$\bf \frac{ \sqrt{5} }{3} \: \: \: \: \: \: \: \: \: \&\: \: \: \: \: \: \: \: \: \frac{3}{ \sqrt{7} }$

• Rationalizing the 2nd fraction,

$\tt \frac{3}{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} } \: \: = \frac{3 \sqrt{7} }{7}$

Therefore,

• Simplified fraction are --

$\bf \frac{ \sqrt{5} }{3} \: \: \: \: \: \: \: \: \: \&\: \: \: \: \: \: \: \: \: \frac{3 \sqrt{7} }{ {7} }$

• Performing cross-mulplication,

$\large \sf 7 \sqrt{5} \: \: \: \: < \: \: \: \: 9 \sqrt{7}$

Thus,

$\bold{ \red{ \frac{3}{ \sqrt{7} }} \: \: \: is \: \: larger.}$