Question

The number which exceeds its positive square root by $12$ is

• A. $9$
• B. $16$
• C. $25$
• D. None of these

Answer 1

The correct option is B $16$

Let the positive number be x according to question,

$\sqrt{x}+12=x$

$\Rightarrow \sqrt{x}=x-12$

Squaring both sides,

$\Rightarrow x=x^2-24x+144$

$x^2-25x+144=0$

$x^2-16x-9x+144=0$

$x(x-16)-9(x-16)=0$

$(x-9)(x-16)=0$

$(x-9)=0$ or $(x-16)=0$

$x=9$ or $x=16$

So, the number is $16$.