The simplified value of (√3 + 1) (10 + 12 ) ( 12 - 2) (5 - √3) is

Answer: Option C

$$\begin{array}{rl}& \left(\sqrt{3}+1\right)\left(10+\sqrt{12}\right)\left(\sqrt{12}-2\right)\left(5-\sqrt{3}\right)\\ & \Rightarrow \left(\sqrt{3}+1\right)\left(10+2\sqrt{3}\right)\left(2\sqrt{3}-2\right)\left(5-\sqrt{3}\right)\\ & \Rightarrow \left(\sqrt{3}+1\right)\times 2\left(5+\sqrt{3}\right)\times 2\left(\sqrt{3}-1\right)\left(5-\sqrt{3}\right)\\ & \Rightarrow 4\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)\left(5-\sqrt{3}\right)\left(5+\sqrt{3}\right)\\ & \Rightarrow 4\left(3-1\right)\left(25-3\right)\left[\left(a+b\right)\left(a-b\right)=a^2-b^2\right]\\ & \Rightarrow 4\times 2\times 22\\ & \Rightarrow 176\\ & \therefore \text{The required answer is }176\end{array}$$