If 5 = 2.236 , then the value of 5 2 \, - 10 5 \, + 125 is equal to = ?

Answer: Option B

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