A) \[2\sqrt{5}\]
B) \[2\sqrt{6}\]
C) \[1+\sqrt{6}\]
D) \[1+\sqrt{5}\]
Correct Answer: A
Solution :
\[\sqrt{11+2\sqrt{30}}-\frac{1}{\sqrt{11+2\sqrt{30}}}\] |
\[=\sqrt{6+5+2\sqrt{5}\sqrt{6}}-\frac{1}{\sqrt{11+2\sqrt{30}}}\] |
\[=\sqrt{{{(\sqrt{6})}^{2}}+{{(\sqrt{5})}^{2}}+2\sqrt{5}\sqrt{6}}-\sqrt{{{(\sqrt{6})}^{2}}+{{(\sqrt{5})}^{2}}+2\sqrt{5}\sqrt{6}}\] |
\[=\sqrt{{{(\sqrt{6}+\sqrt{5})}^{2}}}-\frac{1}{\sqrt{{{(\sqrt{6}+\sqrt{5})}^{2}}}}\] |
\[=\sqrt{6+}\sqrt{5}-\frac{1}{\sqrt{6}+\sqrt{5}}\times \frac{\sqrt{6}-\sqrt{5}}{\sqrt{6}-\sqrt{5}}\] |
\[=\sqrt{6}+\sqrt{5}-\frac{(\sqrt{6}-\sqrt{5})}{6-5}\] |
\[=\sqrt{6}+\sqrt{5}-(\sqrt{6}-\sqrt{5})\] |
\[=\sqrt{6}+\sqrt{5}-\sqrt{6}+\sqrt{5}\] |
\[=2\sqrt{5}\] |
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