Question

find two irrational numbers between 0.7 and 0.77 ​

Answer 1

Two irrational numbers are as follow
0.70700700070000........
0.72722722272222.........

Answer 2

Between any 2 numbers a and b, provided ab is not a perfect square,  

$\sqrt{ab}$ is an irrational number.

Then irrational number between 0.7 and 0.77=  

$\sqrt{0.7*0.77}$ =  $\sqrt{539}$ =0.734166193

And another number =  

$\sqrt{0.7* \sqrt{539} }$  =   $\sqrt{0.7*0.734166193}$ =0.71879976