https://file.aiquickdraw.com/mathbot/file/1729489891239wzhrimwi.jpg

The image contains two square root expressions. Here is a breakdown of both expressions:

1. \( \sqrt{4 + 8h + 4h^2 - 2} \)
2. \( \sqrt{4 + 8h + 4h^2 + 2} \)

Let's simplify both:

### Expression 1:
\( \sqrt{4 + 8h + 4h^2 - 2} \)
- Simplify the constants inside the square root: \( 4 - 2 = 2 \)
- So, this becomes \( \sqrt{2 + 8h + 4h^2} \).

### Expression 2:
\( \sqrt{4 + 8h + 4h^2 + 2} \)
- Simplify the constants inside the square root: \( 4 + 2 = 6 \)
- So, this becomes \( \sqrt{6 + 8h + 4h^2} \).

Both expressions are now simplified.

Would you like me to go further in solving these expressions or provide more details on any specific step?

Here are 5 related questions you might consider:
1. How would you factor the quadratic expression inside the square roots if needed?
2. What is the difference between these two expressions geometrically?
3. How would these expressions behave if you substituted specific values of \(h\)?
4. What methods could be used to simplify these expressions further?
5. Are these expressions solvable analytically or numerically?

**Tip:** When simplifying square root expressions, always check if factoring helps in reducing complexity!

Simplify the square root expressions \( \sqrt{4 + 8h + 4h^2 - 2} \) and \( \sqrt{4 + 8h + 4h^2 + 2} \)

This tutorial simplifies two square root expressions involving quadratic terms: \( \sqrt{4 + 8h + 4h^2 - 2} \) and \( \sqrt{4 + 8h + 4h^2 + 2} \). It breaks down the process of simplifying radical expressions and addresses key algebraic concepts like quadratic equations.

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