If x = √6 - √2, and y = √5 - √3, then which of the following is true?

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Accepted Answer

1. Compute the difference: $x-y=(\sqrt6-\sqrt2)-(\sqrt5-\sqrt3)= (\sqrt6-\sqrt5)+(\sqrt3-\sqrt2)$.  
2. Note that $\sqrt6>\sqrt5$, so $\sqrt6-\sqrt5>0$.  
3. Also $\sqrt3>\sqrt2$, so $\sqrt3-\sqrt2>0$.  
4. Sum of two positive numbers is positive, so $x-y>0$. Thus $x>y$.  
FINAL_ANSWER: c

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