Question

Insert an irrational number between the following:

0.3 and 0.5

Answer 1

Given: Insert an irrational number between 0.3 and 0.5.

Step-wise calculation:

1. Consider the numbers 0.3 and 0.5.

2. We want to find an irrational number x such that 0.3 < x < 0.5

3. One way to do this is to look for a number involving a square root that lies between these two numbers.

4. For example, consider `sqrt(0.15) ≈ 0.3873`, which lies between 0.3 and 0.5.

5. Because `sqrt(0.15)` cannot be expressed as a fraction of integers since 0.15 is not a perfect square rational number, it is irrational.

6. Hence, `sqrt(0.15)` is an irrational number between 0.3 and 0.5.