If n = 7 + 4 3 , then the value of ( n + 1 n ) is:

Answer: Option B

$$\begin{array}{rl}& n=7+4\sqrt{3}\\ & \Rightarrow n=4+3+4\sqrt{3}\\ & \Rightarrow n={\left(2\right)}^2+{\left(\sqrt{3}\right)}^2+2\times 2\times \sqrt{3}\\ & \Rightarrow n={\left(2+\sqrt{3}\right)}^2\\ & \Rightarrow \sqrt{n}=2+\sqrt{3}\\ & \Rightarrow \frac{1}{\sqrt{n}}=2-\sqrt{3}\\ & \therefore \sqrt{n}+\frac{1}{\sqrt{n}}\\ & =2+\sqrt{3}+2-\sqrt{3}\\ & =4\end{array}$$