You can put this solution on YOUR website! sqrt[12+sqrt(12+sqrt(12+...] can be shown as x = sqrt(12+x)
When both sides are squared, the equation becomes x^2 = 12 + x
x^2 = 12 + x
0 = x^2 + x + 12
0 = (x+3)(x-4)
In order for the equation to hold true, x must either be -3, or 4
If we substitute -3 and 4 into x = sqrt(12+x), we find that -3 does not satisfy our equation while 4 does.
Therefore sqrt[12+sqrt(12+sqrt(12+...] is equal to 4
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