Which one of the following is true?

Question

Which one of the following is true?

1. A. sqrt(5) + sqrt(3) sqrt(6) + sqrt(2) (Correct answer)
2. B. sqrt(5) + sqrt(3) < sqrt(6) + sqrt(2)
3. C. sqrt(5) + sqrt(3) = sqrt(6) + sqrt(2)
4. D. (sqrt(5) + sqrt(3))(sqrt(6) + sqrt(2)) = 1

Correct Answer

Option A — sqrt(5) + sqrt(3) sqrt(6) + sqrt(2)

Detailed Solution & Explanation

The correct answer is sqrt(5) + sqrt(3) > sqrt(6) + sqrt(2).

Key Points

• Square both: (sqrt5+sqrt3)^2 = 8+2*sqrt15, (sqrt6+sqrt2)^2 = 8+2*sqrt12.
• Since sqrt15 > sqrt12, sqrt5+sqrt3 > sqrt6+sqrt2.