Question

Write three rational numbers between √3 and √5.

Answer 1

Consider some rational numbers between 3 and 5 such that they are perfect squares.
Let us take, 3.24, 3.61, 4, 4.41 and 4.84 as √3.24 = 1.8, √3.61 = 1.9, √4 = 2, √4.41 = 2.1 and √4.84 = 2.2

Thus we have,
√3 < √3.24 < √3.61 < √4 < √4.41 < √4.84 < √5
⇒ √3 < 1.8 < 1.9 < 2 < 2.1 < 2.2 < √5

⇒ √3 < `18/10 < 19/10 < 2 < 21/10 < 22/10` < √5

⇒ √3 < `9/5 < 19/10 < 2 < 21/10 < 11/5` < √5

Therefore, any three rational numbers between √3 and √5 are :
`9/5, 19/10 and 21/10`