Question

Find an irrational number between 5/7 and 7/9.How many more there may be?

Answer 1

What frustrates me the most about these question is the use of the word the this is indicating that there is just 11 number, there are infinite many. In fact there are uncountable many.

57=456357=4563

79=496379=4963

So we can have:

x632−−−√x632

452<x<492∧x≠462∧x≠472∧x≠482452<x<492∧x≠462∧x≠472∧x≠482

x633−−−√3x6333

453<x<493∧x≠463∧x≠473∧x≠483453<x<493∧x≠463∧x≠473∧x≠483

and so on as irrational numbers.