SSC CGL 24 Aug 2021 Shift 3 Paper

$7698\mathit{x}138\mathit{y}$ is divisible by 72

So, if the number is divisible by 8 and 9 both, the number is divisible by 72 .
Divisibility of 8 , Last 3 digit of number is divisible by 8 , $\frac{38\mathit{y}}{8}$
If we put $\mathit{y}=4$ the number 384 will divisibley by 8 .
Divisibility of 9 ,
If sum of digit is divisible by 9
$\Rightarrow 7+6+9+8+\mathit{x}+1+3+8+4$
$=\frac{46+\mathit{x}}{9}$
Put $\mathit{x}=8$ we get, the number 54 will divisible by 9 .
$\mathit{x}=8,\mathit{y}=4.$
$\therefore \sqrt{4\mathit{x}+\mathit{y}}=\sqrt{4\times 8+4}=\sqrt{36}=6$