ABC26GN1995 · Surds and Indices
Subject: General Aptitude · Chapter: Surds and Indices · Exam: · Marks: · Difficulty:
If $x=5+2 \sqrt{6}$, then $\frac{(x-1)}{\sqrt{x}}$ is equal to
(a)$\sqrt{2}$
(b)$2 \sqrt{2}$
(c)$\sqrt{3}$
(d)$2 \sqrt{3}$
Answer
Explanation
$$\begin{aligned} x & =5+2 \sqrt{6}=3+2+2 \sqrt{6}=(\sqrt{3})^{2}+(\sqrt{2})^{2}+2 \times \sqrt{3} \times \sqrt{2} \\ & =(\sqrt{3}+\sqrt{2})^{2} \end{aligned}$$ Also, $(x-1)=4+2 \sqrt{6}=2(2+\sqrt{6})=2 \sqrt{2}(\sqrt{2}+\sqrt{3})$. $$\therefore \quad \frac{(x-1)}{\sqrt{x}}=\frac{2 \sqrt{2}(\sqrt{3}+\sqrt{2})}{(\sqrt{3}+\sqrt{2})}=2 \sqrt{2} \text {. }$$
Explanation as extracted from the printed page; notation may be imperfect.
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