I.` x^(3) = (root(3)(216))^(3)" "` II.`6y^(2) = 150`

Options

A. If ` x lt y`
B. If `x gt y`
C. If ` x le y`
D. If`x ge y`

Explanation

Let's solve the given equations step by step.

### Problem I: Solve for x in the equation \( x^3 = (\sqrt[3]{216})^3 \)

1. **Understanding the equation**: We start with the equation \( x^3 = (\sqrt[3]{216})^3 \).

2. **Simplifying the right side**: The cube root of 216 can be expressed as:
\[ \sqrt[3]{216} = 6 \]
Therefore, we can rewrite the equation as:
\[ x^3 = 6^3 \]

3. **Taking the cube root of both sides**: Since both sides are cubes, we can take the cube root:
\[ x = 6 \]

### Problem II: Solve for y in the equation \( 6y^2 = 150 \)

1. **Rearranging the equation**: We start with the equation \( 6y^2 = 150 \). To isolate \( y^2 \), divide both sides by 6:
\[ y^2 = \frac{150}{6} \]

2. **Simplifying the right side**: Calculate \( \frac{150}{6} \):
\[ y^2 = 25 \]

3. **Taking the square root of both sides**: To find \( y \), we take the square root:
\[ y = \pm 5 \]

### Conclusion: Comparing x and y

- We found that \( x = 6 \) and \( y = \pm 5 \).
- Since \( 6 > 5 \) and \( 6 > -5 \), we can conclude that \( x > y \).

### Final Answer
Thus, the relationship between \( x \) and \( y \) is:
\[ x > y \]

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