Question

Insert two irrational numbers between the following: 

`1/2` and `13/4`

Answer 1

Given: Insert two irrational numbers between `1/2` and `13/4`.

Step-wise calculation:

1. Convert the given numbers to decimal for easier comparison:

`1/2 = 0.5`,

`13/4 = 3.25`

2. Consider the squares of some numbers lying between these values:

Since 0.5 < x < 3.25, squaring each side, we consider:

`0.5 < sqrt(2) ≈ 1.414 < sqrt(3) ≈ 1.732 < 3.25` 

3. The numbers `sqrt(2)` and `sqrt(3)` are irrational and lie between `1/2` and `13/4`.