$y$ varies directly as the square root of $x$ and $y = 11$ when $x = 4$.

1. Express $y$ as a function of $x$.

   Hint (a):

   Don't forget the '$k$'.
   Substitute the point and solve for '$k$' to get the function.

2. Find $f\left(0\right)$, $f\left(4\right)$, $f\left(8\right)$, and $f\left(a^{2}\right)$.

   Hint (b):

   Use your new function.