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SSC CGL 2025 PYQ — Question 52

SSC CGL - 21 Sep 2025 - Shift 3 • Quantitative Aptitude • Q52

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Simplify: 5+265−26\frac{\sqrt{5+2\sqrt{6}}}{\sqrt{5-2\sqrt{6}}} 

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 5 + 26\sqrt6.

5+265−26\frac{\sqrt{5+2\sqrt{6}}}{\sqrt{5-2\sqrt{6}}}

⇒ (3+2)2(3−2)2\frac{\sqrt{(\sqrt3+\sqrt2)^2}}{\sqrt{(\sqrt3-\sqrt2)^2}} = (3+2)(3−2)\frac{(\sqrt3+\sqrt2)}{(\sqrt3-\sqrt2)}

⇒ (3+2)(3−2)\frac{(\sqrt3+\sqrt2)}{(\sqrt3-\sqrt2)} × (3+2)(3+2)\frac{(\sqrt3+\sqrt2)}{(\sqrt3+\sqrt2)} = (3+2)2(3)2−(2)2\frac{(\sqrt3+\sqrt2)^2}{(\sqrt3)^2-(\sqrt2)^2}

⇒ 3+2+263−2\frac{3+2+2\sqrt6}{3-2} = 5 + 26\sqrt6