If we look at the equation it is $a^{2}+2ab+b^{2}$ where $2ab = 11.98*a$
$a^{2}+2ab+b^{2}$
=$(11.98)^{2}+2ab+(0.02)^{2}$
To make it a perfect square $b=0.02$ and $a=11.98$
$2*11.98*0.02 = 11.98*a$
=>$ a = 0.04$
So the number now will be a perfect square of $12$ ($\because(11.98+0.02)^{2}=12^{2}$)
$\therefore$ option c $0.04$ is the correct answer.