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

2 Answers

  • smci
    Lv 7
    1 decade ago
    Favorite 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".

  • Anonymous
    1 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


    for i=1 to j

    m = sqrt(6+m)


    print m


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