For each of these statement, indicate whether the statement is TRUE or FALSE
If `x^3 = 11`, then `x = root(3)(11)`

Answer

To determine whether the statement "If \( x^3 = 11 \), then \( x = \sqrt[3]{11} \)" is true or false, we can follow these steps:

### Step 1: Understand the equation
We start with the equation given in the statement:
\[ x^3 = 11 \]

### Step 2: Take the cube root of both sides
To isolate \( x \), we take the cube root of both sides of the equation:
\[ x = \sqrt[3]{11} \]

### Step 3: Analyze the result
The expression \( \sqrt[3]{11} \) represents the cube root of 11. This means that if we raise \( \sqrt[3]{11} \) to the power of 3, we should get back 11:
\[ (\sqrt[3]{11})^3 = 11 \]

### Step 4: Conclusion
Since we have shown that taking the cube root of both sides leads us back to the original equation, we can conclude that the statement is true.

Thus, the final answer is:
**TRUE**: If \( x^3 = 11 \), then \( x = \sqrt[3]{11} \).

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