For each of these statement, indicate whether the statement is TRUE or FALSE
If `x^2 = 11`, then `x = sqrt(11)`

Answer

To determine whether the statement "If \( x^2 = 11 \), then \( x = \sqrt{11} \)" is TRUE or FALSE, we can follow these steps:

### Step 1: Start with the equation
Given the equation:
\[ x^2 = 11 \]

### Step 2: Rearrange the equation
We can rearrange this equation to:
\[ x^2 - 11 = 0 \]

### Step 3: Factor the equation
Using the difference of squares identity, we can factor it as:
\[ (x - \sqrt{11})(x + \sqrt{11}) = 0 \]

### Step 4: Set each factor to zero
We can set each factor equal to zero to find the possible values of \( x \):
1. \( x - \sqrt{11} = 0 \) → \( x = \sqrt{11} \)
2. \( x + \sqrt{11} = 0 \) → \( x = -\sqrt{11} \)

### Step 5: Conclusion
From the above steps, we find that \( x \) can be either \( \sqrt{11} \) or \( -\sqrt{11} \). Since the original statement claims that \( x = \sqrt{11} \) without considering the negative root, the statement is FALSE.

### Final Answer
The statement "If \( x^2 = 11 \), then \( x = \sqrt{11} \)" is FALSE.

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