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SSC CGL 2022 PYQ — Question 47

SSC CGL Tier II - Quant - 29 Jan 2022 • Quantitative Aptitude • Q47

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The value of 14−15\frac{1}{4-\sqrt15}-115−14\frac{1}{\sqrt15-\sqrt14}+114−13\frac{1}{\sqrt14-\sqrt13}-113−12\frac{1}{\sqrt13-\sqrt12}+112−11\frac{1}{\sqrt12-\sqrt11}-111−10\frac{1}{\sqrt11-\sqrt10}+110−3\frac{1}{\sqrt10-3}-13−8\frac{1}{3-\sqrt8}is:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 4 -  2√2

 14−15\frac{1}{4-\sqrt15}-115−14\frac{1}{\sqrt15-\sqrt14}+114−13\frac{1}{\sqrt14-\sqrt13}-113−12\frac{1}{\sqrt13-\sqrt12}+112−11\frac{1}{\sqrt12-\sqrt11}-111−10\frac{1}{\sqrt11-\sqrt10}+110−3\frac{1}{\sqrt10-3}-13−8\frac{1}{3-\sqrt8} 

The rationalization form of 14−15\frac{1}{4-\sqrt15} = 4 + 15\sqrt{15}

The rationalization form of115−14\frac{1}{\sqrt15-\sqrt14} = 15\sqrt{15} + 14\sqrt{14}

Similarly, The rationalization form of114−13\frac{1}{\sqrt14-\sqrt13}= 14\sqrt{14} + 13\sqrt{13}

So one can say that,

 The rationalization form of 13−8\frac{1}{3-\sqrt8} = 3 + 8\sqrt{8}

On combining all the forms with respect of their sign we get,

 =  4 + 15\sqrt{15} -   15\sqrt{15} - 14\sqrt{14} + 14\sqrt{14} + 13\sqrt{13} - 13\sqrt{13} - 12\sqrt{12} + 12\sqrt{12} + 11\sqrt{11} - 11\sqrt{11} - 10\sqrt{10} + 10\sqrt{10} + 3 - 3 - 8\sqrt{8}

= 4 - 8\sqrt{8}

= 4 - 2√2.