SSC CGL 2022 PYQ — Question 89

 The correct answer is option 4 i.e. 7 : 8

⇒   $\frac{22 \sqrt2}{4\sqrt2-\sqrt3+\sqrt5}$= a + √5b

On rationalizing the LHS part we get,

⇒   $\frac{22 \sqrt2}{4\sqrt2-\sqrt3+\sqrt5}$= a + √5b

⇒ $\frac{22 \sqrt2 \times(4\sqrt2-\sqrt3-\sqrt5)}{(4\sqrt2-\sqrt3+\sqrt5)(4\sqrt2-\sqrt3-\sqrt5}$

⇒ $\frac{2(88 - 11\sqrt6 - 11\sqrt{10}}{2(15 - 4 \sqrt6)}$

Again on rationalization, we get,

⇒ $\frac{(88 - 11\sqrt6 - 11\sqrt{10}}{(15 - 4 \sqrt6)} \times \frac{15 + 4\sqrt6}{15 + 4\sqrt6}$.