A variant of Ying's trick (manipulating an infinite expression so that the expression appears as a part of itself) can be used in other situations. For example, to evaluate the infinite "continued radical" below, let:

$S = \sqrt { 2 + \sqrt { 2 + \sqrt { 2 + \sqrt { 2 + \ldots } } } }$

Explain why $S = \sqrt { 2 + S }$. Then solve for $S$.