Let x = 6 27 - 63/4 and y = 45 + 605 + 245 80 + 125 , then the value of x2 + y2 is:

Answer: Option A

$$\begin{array}{rl}& x=\text{root}6\text{of}27-\sqrt{6\frac{3}{4}}\\ & x^2={\left({27}^{\frac{1}{6}}-\frac{{27}^{\frac{1}{2}}}{2}\right)}^2\\ & x^2=27^{\frac{2}{6}}+\frac{27}{4}-\frac{2\times {27}^{\frac{1}{6}}\times {27}^{\frac{1}{2}}}{2}\\ & x^2=3+\frac{27}{4}-9\\ & x^2=\frac{3}{4}\\ & y=\frac{\sqrt{45}+\sqrt{605}+\sqrt{245}}{\sqrt{80}+\sqrt{125}}\\ & y=\frac{3\sqrt{5}+11\sqrt{5}+7\sqrt{5}}{4\sqrt{4}+5\sqrt{5}}\\ & y=\frac{7}{3}\\ & y^2=\frac{49}{9}\\ & x^2+y^2=\frac{3}{4}+\frac{49}{9}=\boxed{\frac{223}{36}}\end{array}$$