Question

Find 5 rational numbers between 'root 5/7' and '4/9'

Answer 1

(5/7)*(9/9)=45/63
(4/9)*(7/7)=28/63
5 rational no are 29/63,30/63,31/63,32/63,33/63

Answer 2

Answer:

The five rational numbers which is between $\sqrt { \frac { 5 } { 7 } } \text { and } \sqrt { \frac { 4 } { 9 } }$ is

$\sqrt { \frac { 29 } { 63 } } , \sqrt { \frac { 30 } { 63 } } , \sqrt { \frac { 31 } { 63 } } , \sqrt { \frac { 32 } { 63 } } , \sqrt { \frac { 33 } { 63 } }$

Solution:

Given numbers are $\sqrt { \frac { 5 } { 7 } } \text { and } \sqrt { \frac { 4 } { 9 } }$

To equalize both the terms, take the LCM of 7 and 9.

Hence, $\sqrt \frac {5}{7}$ becomes

$\sqrt { \frac { 5 } { 7 } \times \frac { 9 } { 9 } } = \sqrt { \frac { 45 } { 63 } }$

Similarly, $\sqrt \frac {4}{9}$ becomes

$\sqrt { \frac { 4 } { 9 } \times \frac { 7 } { 7 } } = \sqrt { \frac { 28 } { 63 } }$

Now, we need to find the numbers between  $\sqrt { \frac { 5 } { 7 } } \text { and } \sqrt { \frac { 4 } { 9 } }$ i.e., between $\sqrt { \frac { 28 } { 63 } } \text { and } \sqrt { \frac { 45 } { 63 } }$

Let us take the five rational numbers as,

$\sqrt { \frac { 29 } { 63 } } , \sqrt { \frac { 30 } { 63 } } , \sqrt { \frac { 31 } { 63 } } , \sqrt { \frac { 32 } { 63 } } , \sqrt { \frac { 33 } { 63 } }$