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SSC Selection Post 2022 PYQ — Question 52

SSC Selection Post - Matriculation Level 2022 - 7 Feb 2022 - Shift 1 • Quantitative Aptitude • Q52

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Simplify 5−35+3\sqrt5-\sqrt3\over\sqrt5+\sqrt3 - 5+35−3\sqrt5+\sqrt3\over\sqrt5-\sqrt3.

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Correct answer: D

Explanation

 The correct answer is option 4 i.e. −215-2\sqrt{15}.

Given,  5−35+3\sqrt5-\sqrt3\over\sqrt5+\sqrt3 - 5+35−3\sqrt5+\sqrt3\over\sqrt5-\sqrt3

⇒ (5−3)2−(5+3)2(5+3)(5−3)\frac{(\sqrt{5} - \sqrt{3})^2 - (\sqrt{5} +\sqrt{3})^2}{(\sqrt{5} + \sqrt{3})(\sqrt{5} - \sqrt{3})}

⇒ 8−215−8−2152\frac{8 - 2\sqrt{15} - 8 -2 \sqrt{15}}{2} = −215-2\sqrt{15}