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The expression $\left ( 11.98\times 11.98+11.98\times a+0.02\times 0.02 \right )$ will be a perfect square for $’a’$ equal to _________

$a)0.02$

$b)0.2$

$c)0.04$

$d)0.4$
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+1 vote
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.
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