`sqrt(sqrt(6+sqrt(6+sqrt(6)) ... prop)`   =

Solution

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 3. 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. 6 = 2 `xx` 3 so answer is 3. 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`