insert 5 rational numbers between root 5/7 and 4/9

Question

 how to find rational numbers between root of 5 divided by 7 and 4 divided by 7

 

Answer 1

Good morning Selvi,

 

Could you verify that the two values are √5/7 and 4/9. I don't think it makes sense any other way.

 

√5/7 < x < 4/9

 

square everything

 

5/49 < x² < 16/81

 

get a common denominator for the endvalues so we can compare them

 

405/3969 < x² < 784/3969

 

Choose 5 numbers between 405 and 784 that are perfect squares. 

 

x² = 441/3969, 484/3969, 529/3969, 576/3969, 625/3969

 

x = 21/63 ( which reduces to 1/3), 22/63, 23/63, 24/63, 65/63

 

These are 5 possible answers