Question

Insert five irrational numbers between `2sqrt5` and `3sqrt3`.

Answer 1

We know that `2sqrt5 = sqrt(4 xx 5) = sqrt20` and

`3sqrt3 = sqrt(9 xx 3) = sqrt27`

Thus, We have, `sqrt20 < sqrt21 < sqrt22 < sqrt23 < sqrt24 < sqrt25 < sqrt26 < sqrt27`

So any five irrational numbers between `2sqrt5 "and" 3sqrt3`are :

`sqrt21, sqrt22, sqrt23, sqrt24, "and" sqrt26`