Question

Find a rational number between the following:

`sqrt(18)` and `sqrt(19)`

Answer 1

Given: Find a rational number between `sqrt(18)` and `sqrt(19)`.

Step wise calculation:

1. First, approximate `sqrt(18)` and `sqrt(19)`:

`sqrt(18) = sqrt(9 xx 2)`

= `3sqrt(2) ≈ 3 xx 1.414`

= 4.242 

`sqrt(19) ≈ 4.3589`

2. We want a rational number r such that 4.242 < r < 4.3589

3. Choose a simple rational number (fraction or decimal) in this interval.

For example:  r = 4.3

`r = 43/10`

Clearly, 4.242 < 4.3 < 4.3589

A rational number between `sqrt(18)` and `sqrt(19)` is `43/10`.