Given the values \( x = 4 \), \( y = 5 \), and \( z = -2 \), you need to evaluate the expression:

\[
4\sqrt{x^3} + 40y + 4z
\]

Let's break it down step by step.

1. **Calculate \( x^3 \)**:
   \[
   x^3 = 4^3 = 64
   \]

2. **Calculate \( \sqrt{x^3} \)**:
   \[
   \sqrt{64} = 8
   \]

3. **Multiply by 4**:
   \[
   4 \times 8 = 32
   \]

4. **Calculate \( 40y \)**:
   \[
   40 \times 5 = 200
   \]

5. **Calculate \( 4z \)**:
   \[
   4 \times (-2) = -8
   \]

6. **Add all the terms together**:
   \[
   32 + 200 - 8 = 224
   \]

So, the value of the expression is **224**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the value of the expression if \( y = 6 \) instead of 5?
2. How does the result change if \( z = 3 \)?
3. Can you express the entire equation in terms of one variable, say \( x \)?
4. How would the calculation change if the square root was replaced by a cube root?
5. What would the expression become if all the coefficients were doubled?

**Tip:** Always double-check your calculations when dealing with multiple steps to avoid small errors that can affect the final result.

Learn how to evaluate the expression 4 times the square root of x cubed plus 40 times y plus 4 times z with a step-by-step solution. This problem involves calculating powers, square roots, multiplication, and addition. Suitable for students in Grades 7-9.

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