Simplify, and isolate the radical.
 
Incorrect: Your answer is incorrect.
 − 2

z + 3
 = 	−2

 = 	2

z + 3

 = 	

z + 3


It seems there is a misunderstanding in the problem statement. However, I can guide you through simplifying and isolating the radical step by step. Based on your text, it looks like you're working with an equation involving a square root. Let’s assume the correct expression is:

\[
\sqrt{z + 3} = -2
\]

### Step 1: Isolate the radical
The radical (square root) is already isolated in the equation:

\[
\sqrt{z + 3} = -2
\]

### Step 2: Square both sides
To eliminate the square root, square both sides of the equation:

\[
(\sqrt{z + 3})^2 = (-2)^2
\]

This simplifies to:

\[
z + 3 = 4
\]

### Step 3: Solve for \(z\)
To isolate \(z\), subtract 3 from both sides:

\[
z = 4 - 3
\]

\[
z = 1
\]

### Step 4: Verify the solution
Substitute \(z = 1\) back into the original equation to check if it satisfies the equation:

\[
\sqrt{1 + 3} = \sqrt{4} = 2
\]

However, the original equation states \(\sqrt{z + 3} = -2\). Since the square root function only returns non-negative values, the equation \(\sqrt{z + 3} = -2\) has no real solutions.

**Conclusion**: The equation \(\sqrt{z + 3} = -2\) has no real solutions because the square root of a number cannot be negative.

---

Would you like more details, or do you have any questions? Here are five related questions to explore further:

1. How do we handle square root equations with complex solutions?
2. What are the properties of square root functions?
3. Can we have negative square roots in complex numbers?
4. How do we solve radical equations with higher roots (e.g., cube roots)?
5. What are the steps to simplify radical expressions?

**Tip**: Always check the domain of the function when working with square roots to ensure your solutions are valid.

Learn how to simplify and isolate radicals in algebraic equations with a detailed step-by-step solution. This problem covers key concepts in Algebra, including the properties of square roots and equality. Suitable for students in Grades 8-10.

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