Question

Write two rational numbers between √2 and √3.

Answer 1

We want rational numbers a/b and c/d such that : √2 < `a/b < c/d` < √3
Consider any two rational numbers between 2 and 3 such that they are perfect squares.
Let us take 2.25 and 2.56 as √2.25 = 1.5 and √2.56 = 1.6

Thus we have,
√2 < √2.25 < √2.56 < √3
⇒ √2 < 1.5 < 1.6 < √3

⇒ √2 < `15/10 < 16/10` < √3

⇒ √2 < `3/2 < 8/5` < √3
Therefore any two rational numbers between √2 and √3 are : `3/2 and 8/5`