If `omega` denotes the cube root of unity, then what is the real root of the equaton `x^(3)-27=0` ?

Options

A. `3 omega`
B. `3omega^(2)`
C. `-3omega`
D. `3omega^(3)`

Explanation

To solve the equation \( x^3 - 27 = 0 \) and find the real root, we can follow these steps:

### Step 1: Set the equation to zero
We start with the equation:
\[ x^3 - 27 = 0 \]

### Step 2: Isolate \( x^3 \)
To isolate \( x^3 \), we add 27 to both sides:
\[ x^3 = 27 \]

### Step 3: Take the cube root
Next, we take the cube root of both sides to solve for \( x \):
\[ x = \sqrt[3]{27} \]

### Step 4: Calculate the cube root
We know that \( 27 = 3^3 \), so:
\[ x = \sqrt[3]{3^3} = 3 \]

### Conclusion
The real root of the equation \( x^3 - 27 = 0 \) is:
\[ \boxed{3} \]