A) \[\frac{1}{3}\]
B) \[\frac{2}{3}\]
C) \[\frac{\sqrt{2}}{3}\]
D) \[3\sqrt{2}\]
Correct Answer: A
Solution :
Expression \[=\frac{\sqrt{2}(2+\sqrt{3})}{\sqrt{3}(\sqrt{3}+1)}\times \frac{\sqrt{2}(2-\sqrt{3})}{\sqrt{3}(\sqrt{3}-1)}\] \[=\frac{\sqrt{2}\times \sqrt{2}(2+\sqrt{3})(2-\sqrt{3})}{\sqrt{3}\times \sqrt{3}(\sqrt{3}+1)(\sqrt{3}-1)}\] \[=\frac{2\times (4-3)}{3(3-1)}=\frac{2}{3\times 2}=\frac{1}{3}\]
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