Question

The number which exceeds its positive square root by 12 is
(A) 9
(B) 16
(C) 25
(D) None of these

Answer 1

Hint: Let the number be $x^2$ . Then form the equation in terms of $x^2$ using the information given in the question. It would form a quadratic equation. Solve that quadratic equation using splitting the middle term to get the answer. Remember the root is positive.

Complete step-by-step answer:
It is given in the question that the number exceeds its positive square root by 12.
Let that number be $x^2$
Then, we can write the above statement in mathematical form as
 $x^2=x+12$
Rearranging it we can write
 $x^2-x-12=0$
This is a quadratic equation. We can solve it by using the method of splitting the middle term as
 $x^2-4x+3x-12=0$
By taking common terms out, we get
 $x(x-4)+3(x-4)=0$
By taking common terms out, we get
  $(x-4)(x+3)=0$
 $\Rightarrow x-4=0$ or $x+3=0$
 $x=4$ or $x=-3$
But $x\ne -3$ because we need positive square root of $x^2$
Therefore, $x=4$ is the answer. And hence the required number is $x^2=16$
Therefore, from the above explanation, the correct answer is, option (B) $16$
So, the correct answer is “Option B”.

Note: Here, you need to observe one thing that. Instead of taking the number to be $x$ , we took it to be $x^2$ . The logic behind it was, if we have taken the number to be equal to $x$ . Then its root would have been $\sqrt{x}$ . Then after forming the equation, we would have had to take a square to both sides of the equation and expand it. This would have increased the steps as well as made the solution complex. Just by taking $x^2$ instead of $x$ . We made the solution short and simple.