Let x = √[6 + √{6 + (√6 + .............)}]

=> x = √(6 + x)                                      [ since x = √[6 + √{6 + (√6 + .............)}] ]

Now, squaring on both side, we get

      x² = 6 + x

=> x² - x - 6 = 0

=> x² - 3x + 2x - 6 = 0

=> x(x - 3) + 2(x - 3) = 0

=> (x - 3)*(x + 2) = 0

=> x = 3, -2

Here, x = -2 is not possible because square root of a negative number is not possible.

So, x = 3

So, √[6 + √{6 + (√6 + .............)}] = 3