Hello, nippy!

Here's a way to solve this . . .1. Is there an irrational number between and ?

We have: .

Square: .

We can let equal any number in that interval.

The simplest is: .

By my method, we have: .2. Is there an irrational number between ?

How about 9/2 root of two? . . . . . Yes!

Raise to the 20th power: .

And we can use: .