SSC GD 2025 PYQ — Question 42

 The correct answer is option 4 i.e.  $4({3 - \sqrt{2} })$.

a : b = b : c

a = (3 + $\sqrt{2}$) and b = 2$\sqrt{7}$

c = b²/a​ = ( (2$\sqrt{7}$)²)/( 3 + $\sqrt{2}$)

⇒ c = 28/ ( 3 + $\sqrt{2}$)

Rationalizing denominator

c =  (28 ( 3 - $\sqrt{2}$))/(( 3 + $\sqrt{2}$)( 3 - $\sqrt{2}$))

⇒ c =  (28 ( 3 - $\sqrt{2}$))/(9 - 2) = 4(3 - $\sqrt{2}$)