Question

Insert two irrational numbers between the following:

`3sqrt(5)` and `2sqrt(3)`

Answer 1

Let’s consider the following:

• `3sqrt(5)` is approximately 6.708.
• `2sqrt(3)` is approximately 3.464.

To find two irrational numbers between these, we can choose square roots of numbers that lie between 37 and 38. The square roots of 37 and 38 are irrational and fit nicely between the given numbers.

Thus, the two irrational numbers between `3sqrt(5)` and `2sqrt(3)` are:

• `sqrt(37) ≈ 6.083`
• `sqrt(38) ≈ 6.164`

These numbers are irrational and lie between the approximated values of `3sqrt(5)` and `2sqrt(3)`.