1. The problem is to evaluate the function $f(x) = x^2 \sqrt{4x} + 20$ at $x=0$. 2. The formula given is $f(x) = x^2 \sqrt{4x} + 20$. 3. Substitute $x=0$ into the function: $$f(0) = 0^2 \sqrt{4 \cdot 0} + 20$$ 4. Simplify inside the square root: $$\sqrt{4 \cdot 0} = \sqrt{0} = 0$$ 5. Now the expression becomes: $$f(0) = 0^2 \cdot 0 + 20 = 0 + 20 = 20$$ 6. Therefore, the value of the function at $x=0$ is $20$. Final answer: $f(0) = 20$