If $$\sqrt 5 = 2.236{\text{,}}$$   then the value of $$\frac{{\sqrt 5 }}{2} \, - $$  $$\frac{{10}}{{\sqrt 5 }} \, + $$  $$\sqrt {125} $$  is equal to = ?

$$\eqalign{ & = \frac{{\sqrt 5 }}{2} - \frac{{10}}{{\sqrt 5 }} + \sqrt {125} \cr & = \frac{{{{\left( {\sqrt 5 } \right)}^2} - 20 + 2\sqrt 5 \times 5\sqrt 5 }}{{2\sqrt 5 }} \cr & = \frac{{5 - 20 + 50}}{{2\sqrt 5 }} \cr & = \frac{{35}}{{2\sqrt 5 }} \times \frac{{\sqrt 5 }}{{\sqrt 5 }} \cr & = \frac{{35\sqrt 5 }}{{10}} \cr & = \frac{7}{2} \times 2.236 \cr & = 7 \times 1.118 \cr & = 7.826 \cr} $$