To find the domain of the function $h(x) = 30\sqrt{x - 40}$, we need to determine the values of $x$ for which the expression under the square root is non-negative. This is because the square root function is only defined for non-negative values.

1. Set up the inequality:
   $x - 40 \geq 0$

2. Solve for $x$:
   $x \geq 40$

3. Interpret the result:
   The domain of $h(x)$ is all $x$ values that are greater than or equal to 40.

Final Answer:

The domain of $h(x) = 30\sqrt{x - 40}$ is: $x \geq 40$ or, in interval notation: $[40, \infty)$

Would you like a further breakdown of these steps or have any questions?

---

Here are five related questions to deepen understanding:

1. What is the domain of $f(x) = \sqrt{2x - 10}$?
2. How would the domain change if $h(x)$ was $30 \sqrt{x + 40}$?
3. For the function $g(x) = \sqrt{x - 20} + \sqrt{60 - x}$, what is the domain?
4. If $h(x) = 30\sqrt{40 - x}$, what would the domain be?
5. How does the presence of the square root affect the domain in functions?

Tip: Always check for restrictions in the argument of square roots and denominators when finding domains!