`sqrt(sqrt(2+sqrt(2+sqrt(2)) ... prop)`   =

Solution

let x = `sqrt(sqrt(2+sqrt(2+sqrt(2)) ... prop)` So x = √2+x So x² = 2+x or x²-x-2 =0 or x = -1, 2. 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 bigger one. 2 = 1 `xx` 2 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`