A) \[\sqrt{3}+\sqrt{2}\]
B) \[\sqrt{3}-\sqrt{2}\]
C) \[\sqrt{2}-\sqrt{3}\]
D) \[2\sqrt{2}\]
Correct Answer: A
Solution :
\[5+2\sqrt{6}=3+2+2\times \sqrt{3}\times \sqrt{2}\] \[={{(\sqrt{3})}^{2}}+{{(\sqrt{2})}^{2}}+2\times \sqrt{3}\times \sqrt{2}={{(\sqrt{3}+\sqrt{2})}^{2}}\] \[\therefore \]\[\sqrt{5+2\sqrt{6}}=\sqrt{{{(\sqrt{3}+\sqrt{2})}^{2}}}=\sqrt{3}+\sqrt{2}\]
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