Question

Insert 3 irrational numbers between 11 and 12.
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Answer 1

The number of irrational numbers between 12 an 13 is uncountable.

(The number of irrationals between anything an anything else is uncountable.)

Here is one set of three irrationals between 12 and 13:

$12 + \frac{\sqrt{2}}{1000}$

$12 + \frac{\sqrt{3}}{1000}$

$12 + \frac{\sqrt{5}}{1000}$

Here is another set of three irrationals between 12 and 13:

$12 + \frac{\pi}{100}$

$12.1 + \frac{\pi}{100}$

$12.2 + \frac{\pi}{100}$