Square root value

$\begin{aligned} x\sqrt x + 64 y\sqrt y & = 539 & \small \color{#3D99F6} \text{Given} \\ \color{#3D99F6} (\sqrt x)^3 + (4\sqrt y)^3 & = 539 & \small \color{#3D99F6} \text{Since }a^3+b^3 = (a+b) (a^2 - ab + b^2) \\ \color{#D61F06} (\sqrt x + 4\sqrt y)\color{#3D99F6} (x - 4\sqrt{xy} + 16y) & = 539 & \small \color{#D61F06} \text{Given that }\sqrt x + 4\sqrt y = 11 \\ \implies x + 16 y - 4\sqrt{xy} & = \frac {539}{\color{#D61F06}11} \\ & = \boxed {49} \end{aligned}$

$\sqrt{x}+4 \sqrt{y}=11\land x \sqrt{x}+64 y \sqrt{y}=539 \Rightarrow \left\{x\to 64,y\to \frac{9}{16}\right\},\{x\to 9,y\to 4\}$ . Both solutions imply that the value of $-4 \sqrt{x y}+x+16 y$ is $49$ .