Which of the following is true?
2016
Which of the following is true?
- A.
\sqrt{3}+\sqrt{7}=\sqrt{10}
- B.
\sqrt{3}+\sqrt{7}\leqslant \sqrt{10}
- C.
\sqrt{3}+{\sqrt{7}< \sqrt{10}}
- D.
\sqrt{3}+{\sqrt{7}> \sqrt{10}}
Attempted by 43 students.
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Correct answer: D
To determine the true statement, compare the sum of square roots to a single square root. Squaring both sides reveals that the squared sum equals ten plus twice the square root of twenty-one, which is strictly greater than ten. Consequently, the inequality stating the sum is greater than the single root holds true, confirming the third option as correct.