We have the variable y, that is proportional to √x.
We can express as:
[tex]y=k\cdot\sqrt[]{x}[/tex]We know that y = 22 when x = 576.
Then, we can find the constant of proportionality k replacing y and x with the values:
[tex]\begin{gathered} y=k\sqrt[]{x} \\ k=\frac{y}{\sqrt[]{x}} \\ k=\frac{22}{\sqrt[]{576}} \\ k=\frac{22}{24} \\ k=\frac{11}{12} \end{gathered}[/tex]Knowing the value of k, we can calculate the value of y when x = 331776 as:
[tex]\begin{gathered} y=\frac{11}{12}\sqrt[]{x} \\ y=\frac{11}{12}\sqrt[]{331776} \\ y=\frac{11}{12}\cdot576 \\ y=528 \end{gathered}[/tex]Answer: y = 528
