A) 1.4144
B) 2.8284
C) 28.284
D) 2.4142
Correct Answer: B
Solution :
Given expression \[=2\sqrt{2}+\sqrt{2}+\frac{1}{2+\sqrt{2}}+\frac{1}{\sqrt{2}-2}\] \[=2\sqrt{2}+\sqrt{2}+\left( \frac{1}{2+\sqrt{2}}-\frac{1}{2-\sqrt{2}} \right)\] \[=2\sqrt{2}+\sqrt{2}+\left( \frac{2-\sqrt{2}-2-\sqrt{2}}{(2+\sqrt{2})(2-\sqrt{2})} \right)\] \[=2\sqrt{2}+\sqrt{2}+\frac{-2\sqrt{2}}{4-2}\] \[=2\sqrt{2}+\sqrt{2}-\sqrt{2}=2\sqrt{2}\] \[=2\times 1.4142=2.8284\]
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