Query Detail : SSC CGL Tier I

If x = 5 + 2 under root 6, then find the value of under root x – 1/ under root x. My answer: 2 under root 2. Correct answer: 8
Garima,   November 17th 2019,  
SSC CGL Tier I


x = 5+ 2`sqrt(6)`  = 3+2 +2`sqrt(6)`

 x = `(sqrt(3) + sqrt(2))^2` 

So `sqrt(x)` = `(sqrt(3) + sqrt(2))` 

and 1/`sqrt(x)` = `(sqrt(3) - sqrt(2))` 

So  `sqrt(x)` -  1/`sqrt(x)` = `(sqrt(3) + sqrt(2))` - `(sqrt(3) - sqrt(2))` = 2`sqrt(2)`