`sqrt(sqrt(6-sqrt(6-sqrt(6)) ... prop)`  = ?

let x = `sqrt(sqrt(6-sqrt(6-sqrt(6)) ... prop)` So x = √6-x So x² = 6-x or x²+x-6 = 0 or x = 2,-3. x cannot be negative so final answer is 2. Alternate Method : For these type of questions of positive infinite, just brake the number in the product of two consecutive number and answer will be smaller one. 6 = 2 `xx` 3 so answer is 2. If the given number cannot be break in two consecutive numbers then for x=   `sqrt(sqrt(N+sqrt(N+sqrt(N)) ... prop)` , use this shortcut ,  x =  `{-1 + sqrt(4N+1)}/2`