Simplify the following: [(-4 ± (8)^(1/2))/2]

To simplify the expression:

\[
\frac{-4 \pm \sqrt{8}}{2}
\]

### Step 1: Simplify the square root
We can simplify \(\sqrt{8}\) as follows:

\[
\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}
\]

### Step 2: Substitute the simplified square root
Substituting \(\sqrt{8} = 2\sqrt{2}\) into the original expression:

\[
\frac{-4 \pm 2\sqrt{2}}{2}
\]

### Step 3: Simplify the fraction
Now, divide both terms in the numerator by 2:

\[
\frac{-4}{2} \pm \frac{2\sqrt{2}}{2} = -2 \pm \sqrt{2}
\]

### Final Answer:
The simplified expression is:

\[
-2 \pm \sqrt{2}
\]

Do you want details or have any questions?

Here are 5 related questions:
1. How do you simplify radicals like \(\sqrt{8}\)?
2. How can you solve quadratic equations using the quadratic formula?
3. What does the \(\pm\) symbol mean in mathematics?
4. How do you factor quadratic equations?
5. What is the process for simplifying complex fractions?

**Tip:** Always simplify square roots by factoring them into perfect squares.

Learn how to simplify the expression (-4 ± √8) / 2 through step-by-step instructions. This problem covers key algebraic concepts such as square root simplification and fraction reduction. Ideal for students in Grades 8-10.

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