Question

Find an irrational number between `sqrt(6)` and `sqrt(10)`.

Answer 1

Given: Find an irrational number between `sqrt(6)` and `sqrt(10)`.

Step-wise calculation:

1. We know `sqrt(6)` and `sqrt(10)` are both irrational numbers.

2. Consider the number `sqrt(7)`.

Since 6 < 7 < 10, it follows that `sqrt(6) < sqrt(7) < sqrt(10)`.

3. `sqrt(7)` is an irrational number as 7 is not a perfect square.

4. Therefore, `sqrt(7)` lies between `sqrt(6)` and `sqrt(10)` and is irrational.