Question

Find an irrational number between 3 and `sqrt(15)`.

Answer 1

Given: We are asked to find how `sqrt(10)` is an irrational number between 3 and `sqrt(15)`.

Stepwise calculation:

1. Check the approximate values:

3 = 3.000

`sqrt(10) ≈ 3.162`

`sqrt(15) ≈ 3.873`

2. Since `3 < sqrt(10) < sqrt(15), sqrt(10)` lies strictly between 3 and `sqrt(15)`.

3. `sqrt(10)` is irrational because 10 is not a perfect square.

Therefore, `sqrt(10)` is an irrational number between 3 and `sqrt(15)`.