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

Answer 1

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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".

Source(s): http://en.wikipedia.org/wiki/Nested_radical#Infini...

Answer 2

The previous answer is exactly right

if you have the ability to program

try this program written in RobotBASIC

(http://www.robotbasic.com)/

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