Question

Find a rational number between the following:

`sqrt(2)` and `sqrt(3)`

Answer 1

Given: Find a rational number between `sqrt(2)` and `sqrt(3)`.

Stepwise calculation:

1. Square both numbers to work in terms of rational numbers:

`(sqrt(2))^2 = 2`,

`(sqrt(3))^2 = 3`

2. Choose any rational number between 2 and 3.

For example, take 2.25 which lies between 2 and 3.

3. Since 2 < 2.25 < 3, take the square root of `sqrt(2.25) = 1.5`.

4. Because 1.5 is a rational number and satisfies:

 `sqrt(2) < 1.5 < sqrt(3)`, 1.5 is a rational number between `sqrt(2)` and `sqrt(3)`.

A rational number between `sqrt(2)` and `sqrt(3)` is 1.5.

Hence, 1.5 is a rational number such that `sqrt(2) < 1.5 < sqrt(3)`.