`sqrt(sqrt(56-sqrt(56-sqrt(56)) ... prop)`  = ?

let x = `sqrt(sqrt(56-sqrt(56-sqrt(56)) ... prop)` So x = √56-x So x² = 56-x or x²+x-56 = 0 or x = 7,-8. x cannot be negative so final answer is 7. 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. 56 = 7 `xx` 8 so answer is 7. 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`