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.