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SSC CGL 2020 PYQ — Question 21

SSC CGL Tier II - Quant - 18 Nov 2020 • Quantitative Aptitude • Q21

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If x =−3+3+87+43\sqrt{-\sqrt3 + \sqrt{3 + 8\sqrt{7 + 4\sqrt3}}}  where x > 0, then the value of x is equal to:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 2

7 + 43\sqrt3 = 4 + 3 + 2 × 2 × 3\sqrt3 = (2 + 3\sqrt3)2

⇒ −3+3+87+43\sqrt{-\sqrt3 + \sqrt{3 + 8\sqrt{7 + 4\sqrt3}}} can be written as,

⇒ −3+3+8(2+3)\sqrt{-\sqrt3 + \sqrt{3 + 8(2 + \sqrt3)}}

⇒ −3+3+16+83\sqrt{-\sqrt3 + \sqrt{3 +16 + 8\sqrt3}}

⇒  −3+(4+3)2\sqrt{-\sqrt3 + \sqrt{(4+\sqrt3)^2}}

= 4\sqrt4 

= 2.