A) \[3+\sqrt{5}\]
B) \[3+\sqrt{5}\]
C) \[5+\sqrt{3}\]
D) \[3+2\sqrt{5}\]
Correct Answer: B
Solution :
\[14+6\sqrt{5}=14+2\times 3\times \sqrt{5}\] \[=9+5+2\times 3\times \sqrt{5}\] \[={{(3)}^{2}}+{{(\sqrt{5})}^{2}}+2\times 3\times \sqrt{5}\] \[={{(3+\sqrt{5})}^{2}}\] \[\therefore \] \[\sqrt{14+6\sqrt{5}}=\sqrt{{{\left( 3+5 \right)}^{2}}}\] \[=3+\sqrt{5}\]
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