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

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  • 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

    (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

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