ABC26GN1958 · Surds and Indices
Subject: General Aptitude · Chapter: Surds and Indices · Exam: 2007 · Marks: · Difficulty:
$\sqrt{8-2 \sqrt{15}}$ is equal to
(a)$3-\sqrt{5}$
(b)$\sqrt{5}-\sqrt{3}$
(c)$5-\sqrt{3}$
(d)$\sqrt{5}+\sqrt{3}$
Answer
Explanation
$$\begin{aligned} \sqrt{8-2 \sqrt{15}} & =\sqrt{5+3-2 \times \sqrt{5} \times \sqrt{3}} \\ & =\sqrt{(\sqrt{5})^{2}+(\sqrt{3})^{2}-2 \times \sqrt{5} \times \sqrt{3}} \\ & =\sqrt{(\sqrt{5}-\sqrt{3})^{2}}=(\sqrt{5}-\sqrt{3}) \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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