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Question 29

$$n$$ is a natural number. The square root of the sum of the square of $$n$$ and 19 is equal to the next natural number to $$n$$. The value of $$n$$ is


Correct Answer: 9

Solution

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The condition gives $$\sqrt{n^2+19}=n+1$$, so $$n^2+19=n^2+2n+1$$, which simplifies to $$2n=18$$, giving $$n=9$$.

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