6^2 + 7^2 + 8^2 + 9^2 + 10^2 7 + 4 3 - 4 + 2 3 is equal to = ?

Answer: Option A

$$\begin{array}{rl}& \frac{6^2+7^2+8^2+9^2+{10}^2}{\sqrt{7+4\sqrt{3}}-\sqrt{4+2\sqrt{3}}}\\ & \Rightarrow \frac{6^2+7^2+8^2+9^2+{10}^2}{\sqrt{{\left(2+\sqrt{3}\right)}^2}-\sqrt{{\left(\sqrt{3}+1\right)}^2}}\\ & \Rightarrow \frac{6^2+7^2+8^2+9^2+{10}^2}{2+\sqrt{3}-\sqrt{3}-1}\\ & \Rightarrow 6^2+7^2+8^2+9^2+10^2\\ & \Rightarrow 36+49+64+81+100\\ & \Rightarrow 330\end{array}$$