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An infinitely nested radical is a nested radical in which a given number is infinitely nested. For example, ${\displaystyle {\sqrt {3+{\sqrt {3+{\sqrt {3+\ldots }}}}}}}$. Perhaps the most famous infinitely nested radical is ${\displaystyle {\sqrt {1+{\sqrt {1+{\sqrt {1+\ldots }}}}}}=\phi }$, the golden ratio. An infinitely nested radical works out to an integer if the number nested within is an integer of the form ${\displaystyle n^{2}-n}$ (see A002378), namely ${\displaystyle n}$, e.g., ${\displaystyle {\sqrt {12+{\sqrt {12+{\sqrt {12+\ldots }}}}}}=4}$.