Aptitude Question ID: 107046

Find out the value of : \sqrt{5+2\sqrt{6}}-\frac{1}{\sqrt{5+2\sqrt{6}}}
[A]1+\sqrt{5}
[B]\sqrt{5}-1
[C]2\sqrt{2}
[D]2\sqrt{3}

\mathbf{2\sqrt{2}}
\because \sqrt{5+2\sqrt{6}} = \sqrt{3+2+2\times \sqrt{3}\times \sqrt{2}}
= \sqrt{(\sqrt{3}+\sqrt{2})^{2}}
= \sqrt{3}+\sqrt{2}
\therefore \frac{1}{\sqrt{5+2\sqrt{6}}} = \sqrt{3}-\sqrt{2}
\therefore \sqrt{5+2\sqrt{6}}-\frac{1}{\sqrt{5+2\sqrt{6}}} =  \sqrt{3}+\sqrt{2}-\sqrt{3}+\sqrt{2}= 2\sqrt{2}
Hence option [C] is correct answer.

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