SSC CGL 2025 PYQ — Question 54

The correct answer is option 2 i.e. $\sqrt{6}$.

$\frac{\sqrt{5 + 2\sqrt{6}} + \sqrt{5 - 2\sqrt{6}}}{\sqrt{2}}$

$=\frac{\sqrt{3 +2+ 2\sqrt{3}\sqrt2} + \sqrt{3+2 - 2\sqrt{3}\sqrt2}}{\sqrt{2}}$

$=\frac{\sqrt{(\sqrt3+\sqrt2)^2}+\sqrt{(\sqrt3-\sqrt2)^2}}{\sqrt2}$

$=\frac{\sqrt3+\sqrt2+\sqrt3-\sqrt2}{\sqrt2}$

$=\frac{2\sqrt3}{\sqrt2}$

$=\sqrt3 \times \sqrt2$

$=\sqrt{6}$