( 4 + 7 ), expressed as a perfect square, is equal to = ?

Answer: Option C

$$\begin{array}{rl}& \left(4+\sqrt{7}\right)\\ & =\frac{7}{2}+\frac{1}{2}+2\times \frac{\sqrt{7}}{\sqrt{2}}\times \frac{1}{\sqrt{2}}\\ & ={\left(\frac{\sqrt{7}}{\sqrt{2}}\right)}^2+{\left(\frac{1}{\sqrt{2}}\right)}^2+2\times \frac{\sqrt{7}}{\sqrt{2}}\times \frac{1}{\sqrt{2}}\\ & ={\left(\frac{\sqrt{7}}{\sqrt{2}}+\frac{1}{\sqrt{2}}\right)}^2\\ & =\frac{1}{2}{\left(\sqrt{7}+1\right)}^2\end{array}$$