ABC26GN1437 · Square Roots and Cube Roots
Subject: General Aptitude · Chapter: Square Roots and Cube Roots · Exam: 2007 · Marks: · Difficulty:
$\left(2+\sqrt{2}+\frac{1}{2+\sqrt{2}}+\frac{1}{\sqrt{2}-2}\right)$ simplifies to
(a)$2-\sqrt{2}$
(b)2
(c)$2+\sqrt{2}$
(d)$2 \sqrt{2}$
Answer
Explanation
Given exp. $=(2+\sqrt{2})+\frac{1}{(2+\sqrt{2})} \times \frac{(2-\sqrt{2})}{(2-\sqrt{2})}$ $$\begin{aligned} & -\frac{1}{(2-\sqrt{2})} \times \frac{(2+\sqrt{2})}{(2+\sqrt{2})} \\ & =(2+\sqrt{2})+\frac{(2-\sqrt{2})}{(4-2)}-\frac{(2+\sqrt{2})}{(4-2)} \\ & =(2+\sqrt{2})+\frac{1}{2}(2-\sqrt{2})-\frac{1}{2}(2+\sqrt{2})=2 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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