SSC CGL 2022 PYQ — Question 28

The correct answer is option 3 i.e. 29.

$\frac{\sqrt{38-5\sqrt{3}}}{\sqrt{26+7\sqrt{3}}}=\frac{a+b\sqrt{3}}{23}$

On rationalizing the LHS part we get,

$\frac{\sqrt{38-5\sqrt{3}}}{\sqrt{26+7\sqrt{3}}} \times \sqrt{\frac{26-7\sqrt{3}}{26-7\sqrt{3}}}$

$\sqrt{ \frac{1093 - 396\sqrt3}{529}} = \frac{a + b\sqrt3}{23}$

$\sqrt{1093 - 396\sqrt3} = a + b\sqrt3$

On squaring both sides we get,

1093 - 396$\sqrt3$ = a² + 3b²  + 2ab$\sqrt3$

On factorizing the given expression we get,

(-11)² + (18)² - 2 × -11 × 18 =   a² + 3b²  + 2ab$\sqrt3$

On comparing we get,

a = -11 and b = 18

b - a = 18 - (-11) = 29.