SSC GD 2025 PYQ — Question 51

The correct answer is option 4 i.e.  2$\sqrt{7-\sqrt5}$.

Mean proportional between a and b = $\sqrt {a × b}$

a = 4 + √5

b = 12 − 2√20 = 12 − 4√5

⇒ (4 + √5)(12 − 4√5)

⇒ 48 − 16√5 + 12√5 − 20

⇒ 28 − 4√5

So, mean proportional = 2$\sqrt{7-\sqrt5}$