I.` a^(2) + 72 = 108`
II.` b^(3) + 581 = 365`

Options

A. if `a gt b`
B. if` a ge b`
C. if a = b or no relation can be established between a and b.
D. if` a le b`

Explanation

To solve the equations step by step, we will address each equation separately.

### Step 1: Solve the first equation \( a^2 + 72 = 108 \)

1. **Isolate \( a^2 \)**:
\[ a^2 = 108 - 72 \]
\[ a^2 = 36 \]

**Hint**: To isolate a variable, you can subtract or add the same value from both sides of the equation.

2. **Take the square root of both sides**:
\[ a = \pm \sqrt{36} \]
\[ a = \pm 6 \]

**Hint**: Remember that taking the square root of a number gives both a positive and a negative solution.

### Step 2: Solve the second equation \( b^3 + 581 = 365 \)

1. **Isolate \( b^3 \)**:
\[ b^3 = 365 - 581 \]
\[ b^3 = -216 \]

**Hint**: Similar to the first equation, isolate the variable by performing the same operation on both sides.

2. **Take the cube root of both sides**:
\[ b = \sqrt[3]{-216} \]
\[ b = -6 \]

**Hint**: The cube root of a negative number is negative, so remember this when solving for odd powers.

### Step 3: Compare the values of \( a \) and \( b \)

- From the first equation, we found \( a = 6 \) or \( a = -6 \).
- From the second equation, we found \( b = -6 \).

Now we compare:
- If \( a = 6 \), then \( a > b \) since \( 6 > -6 \).
- If \( a = -6 \), then \( a = b \) since both are equal to -6.

Thus, we can conclude that \( a \) is greater than or equal to \( b \).

### Final Conclusion:
The correct option is that \( a \geq b \).

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