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To address the equation provided:

\[
y = \sqrt[3]{x^2}
\]

with the conditions \( y = 0 \) and \( x = 1 \).

1. First, let's analyze the condition \( y = 0 \):

Given \( y = \sqrt[3]{x^2} \),

\[ 0 = \sqrt[3]{x^2} \]

This implies that \( x^2 = 0 \), hence \( x = 0 \).

So, when \( y = 0 \), \( x \) must be 0.

2. Now, let's analyze the condition \( x = 1 \):

Given \( x = 1 \),

\[ y = \sqrt[3]{1^2} = \sqrt[3]{1} = 1 \]

So, when \( x = 1 \), \( y = 1 \).

Therefore, the conditions show the following points:
- When \( y = 0 \), \( x = 0 \)
- When \( x = 1 \), \( y = 1 \)

Do you have any questions or would you like further details on this problem? Here are some additional questions you might consider:

1. How can you find the derivative of \( y = \sqrt[3]{x^2} \)?
2. What is the behavior of the function \( y = \sqrt[3]{x^2} \) as \( x \) approaches infinity?
3. How do you plot the graph of \( y = \sqrt[3]{x^2} \)?
4. What are the critical points of the function \( y = \sqrt[3]{x^2} \)?
5. How does the function \( y = \sqrt[3]{x^2} \) compare to \( y = x^2 \)?

**Tip:** When solving equations involving roots and powers, always check for potential extraneous solutions and ensure the domain is properly considered.

Learn how to solve the equation y = cube root of (x^2) with a detailed step-by-step solution. This problem covers equations involving roots and powers, including cube roots and powers. Suitable for students in Grades 10-12.

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