Question:
I have been asked to solve the following equation.
Square root 6 + (Square root 6 + (Square root 6.....to infinity
I was given the answer of 3 but need to find the answer. Is there a name
for this function.

Replies:
Expressions such as these are called "nested radicals". For this to equal
an integer = x (in your case, 3) the following relation between 'x' and the
number under the radical, call it 'n' must hold: n = x(x-1)

In your case this is: 6 = 3*(3-1) = 3*2 = 6.

You can find a starting point on studying these mathematical oddities in:
"CRC Concise Encyclopedia of Mathematics" edited by Eric W. Weisstein.

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