Question : Which of the following is true?
Option 1: $\sqrt 5 + \sqrt 3 > \sqrt 6 + \sqrt 2$
Option 2: $\sqrt 5 + \sqrt 3 < \sqrt 6 + \sqrt 2$
Option 3: $\sqrt 5 + \sqrt 3 = \sqrt 6 + \sqrt 2$
Option 4: $(\sqrt 5 + \sqrt 3 ) (\sqrt 6 + \sqrt 2 )= 1$
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Correct Answer: $\sqrt 5 + \sqrt 3 > \sqrt 6 + \sqrt 2$
Solution :
Squaring both terms
$\sqrt 5 + \sqrt 3$, $\sqrt 6 + \sqrt 2$
So, $(\sqrt 5 + \sqrt 3)^2 = 5 + 3 + 2\sqrt 15 = 8 + 2\sqrt 15$
Also, $(\sqrt 6 + \sqrt 2)^2 = 6 + 2 + 2\sqrt 12 = 8 + 2\sqrt 12$
Clearly, $\sqrt 5 + \sqrt 3 > \sqrt 6 + \sqrt 2$
Hence, the correct answer is $\sqrt 5 + \sqrt 3 > \sqrt 6 + \sqrt 2$.
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