Step 1: Write the variation equation. "x varies directly as y and inversely as the square root of z" means that $x$ is proportional to $y$ and inversely proportional to $\sqrt{z}$. We introduce a constant of proportionality, $k$. $$x = \frac{ky}{\sqrt{z}}$$ Step 2: Use the given values to find the constant $k$. We are given $x=300$ when $y=65$ and $z=25$. Substitute these values into the equation: $$300 = \frac{k(65)}{\sqrt{25}}$$ $$300 = \frac{65k}{5}$$ $$300 = 13k$$ Divide by 13 to solve for $k$: $$k = \frac{300}{13}$$ Step 3: Write the specific variation equation with the found $k$. $$x = \frac{\frac{300}{13}y}{\sqrt{z}}$$ $$x = \frac{300y}{13\sqrt{z}}$$ Step 4: Calculate the value of $x$ when $y=468$ and $z=144$. Substitute $y=468$ and $z=144$ into the equation: $$x = \frac{300(468)}{13\sqrt{144}}$$ $$x = \frac{300 \times 468}{13 \times 12}$$ $$x = \frac{140400}{156}$$ $$x = 900$$ The value of $x$ when $y=468$ and $z=144$ is $\boxed{\textbf{900}}$. That's 2 down. 3 left today — send the next one.