how to find sqrt(6 + sqrt (6 +sqrt (6 +sqrt (6 +sqrt (6 +....?
- smciLv 71 decade agoFavorite Answer
Let x = √(6+√(6+√(6+...)))
Then note that since the RHS repeats infinitely:
x = √(6+x)
x² = 6+x
x² -x -6=0
(x-3)(x+2) = 0
x = 3 (or -2, which is not allowed by convention)
A pretty underwhelming representation for 3.
These things are called "Infinitely nested radicals".
- Anonymous1 decade ago
The previous answer is exactly right
if you have the ability to program
try this program written in RobotBASIC
The program will print the result for nesting
up to 20 levels and you should see how it should tend
for j=2 to 20
for i=1 to j
m = sqrt(6+m)