SSC CGL 2019 PYQ — Question 35

The correct answer is option 4 i.e. 223/36

x = ${27}^{1/6} - {\sqrt{6 {3\over4}}}$

= ${\sqrt 3} - {\sqrt{27\over4}}$

= ${\sqrt 3} - {3\over2}{\sqrt{3}}$

= $- {{\sqrt{3}}}\over 2$

x² = 3/4

y = ${{\sqrt {45}} + {\sqrt {605}} +{\sqrt {245}}}\over {{\sqrt {80}}+ {\sqrt {125}}}$

y = ${3{\sqrt {5}} + {11\sqrt {5}} +{7\sqrt {5}}}\over {{4\sqrt {5}}+ {5\sqrt {5}}}$

y = ${21{\sqrt {5}}}\over {9\over5}$

y² = 2205/405 = 49/9

Now,  x² + y² = 3/4 + 49/9 = (196 + 27)/36 = 223/36