## Trending News

Promoted

# how to find sqrt(6 + sqrt (6 +sqrt (6 +sqrt (6 +sqrt (6 +....?

### 2 Answers

Relevance

- 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

towards 3

for j=2 to 20

m=sqrt(6)

for i=1 to j

m = sqrt(6+m)

next

print m

next

Still have questions? Get your answers by asking now.