Question

How to find 2 irrational no.s between 2016 and 2017

Answer 1

You can find two irrational numbers $r,s$ between 0 and 1.

Then, you'll have

$2016 < 2016+r < 2017,\quad 2016 < 2016+s < 2017$

And both $2016+r$ and $2016+s$ will be irrational, because they are the sum of a rational number (2016) and an irrational number (r or s).

Finally, in order to find two such numbers, you can start with any irrational number, and scale it down until it lies between 0 and 1.

For example, you can start from $\sqrt{2}\approx 1.4142$ and divide it by any integer greater than 2, say that we choose

$r = \dfrac{\sqrt{2}}{7}$

$s = \dfrac{\sqrt{2}}{4}$

So, the two irrational numbers between 2016 and 2017 are

$2016 + \dfrac{\sqrt{2}}{7},\quad 2016 + \dfrac{\sqrt{2}}{4}$