\sqrt 7=2+\frac 1{1+\frac 1{\frac 1 {\frac{\sqrt 7+2}3-1}}}=2+\frac 1{1+\frac 1{\frac 3 {\sqrt 7-1}}}=2+\frac 1{1+\frac 1{\frac {3(\sqrt 7+1)}6}}=2+\frac 1{1+\frac 1{\frac {\sqrt 7+1}2}}