If a, b and c are the sides of a triangle ABC, then \sqrt{a}+\sqrt{b}-\sqrt{c} is <strong>ALWAYS</strong> :
- A. Negative
- B. Positive ✓
- C. Non-negative
- D. Non-positive
Correct Answer: B. Positive
Explanation
By the triangle inequality, a+b \gt c. Squaring the sum of the roots: (\sqrt{a}+\sqrt{b})^2 = a+b+2\sqrt{ab}. Since a+b \gt c, then a+b+2\sqrt{ab} \gt c. Hence, \sqrt{a}+\sqrt{b} \gt \sqrt{c}, meaning \sqrt{a}+\sqrt{b}-\sqrt{c} is strictly positive.
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