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

Last updated date: 10th Sep 2024
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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.

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.