Insert 3 rational numbers between
and
using mean method​.​

Step-by-step explanation:

If you have two numbers x and y, their geometric mean is defined as

Let that number be m, and let x be the smallest of the two numbers.

You know for sure that

Since

And

With equality holding if and only if x=y.

So, we can use the geometric mean to generate numbers which are for sure between two desired values. For example:

The middle term is of course irrational, since it's equal to

Now we can do the same thing with our newfound value which we know to be between 1/4 and 1/5:

And

step-by-step explanation: