A) \[2\sqrt{2}\]
B) \[3\sqrt{2}\]
C) \[2\sqrt{3}\]
D) \[3\sqrt{3}\]
Correct Answer: C
Solution :
| \[x=5+2\sqrt{6}\] |
| \[\therefore \]\[\frac{1}{x}=\frac{1}{5+2\sqrt{6}}=\frac{5-2\sqrt{6}}{(5+2\sqrt{6})(5-2\sqrt{6})}\] |
| \[=\frac{5-2\sqrt{6}}{25-24}=5-2\sqrt{6}\] |
| \[\therefore \]\[{{\left( \sqrt{x}+\frac{1}{\sqrt{x}} \right)}^{2}}=+\frac{1}{x}+2\] |
| \[=5+2\sqrt{6}+5-2\sqrt{6}+2=12\] |
| \[\therefore \] \[\sqrt{x}+\frac{1}{\sqrt{x}}=\sqrt{12}=2\sqrt{3}\] |
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