The equation \(\sqrt{8} = \sqrt{2} + \sqrt{2}\) is incorrect. Let's analyze why:

1. **Calculate \(\sqrt{8}\):**
   \[
   \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}.
   \]

2. **Calculate \(\sqrt{2} + \sqrt{2}\):**
   \[
   \sqrt{2} + \sqrt{2} = 2\sqrt{2}.
   \]

3. **Comparing Both Sides:**
   Both sides simplify to \(2\sqrt{2}\), so actually, the statement is true, but it's more precise to write it as:
   \[
   \sqrt{8} = 2\sqrt{2}.
   \]

Thus, while the expression \(\sqrt{8} = \sqrt{2} + \sqrt{2}\) is technically correct in terms of value, the proper simplification of \(\sqrt{8}\) is \(2\sqrt{2}\).

Would you like to dive deeper into square root properties or any other related topics?

### Related Questions:
1. What is the difference between simplifying and approximating square roots?
2. How do you add or subtract square roots with different radicands?
3. Can you explain the properties of square roots in algebraic expressions?
4. How can you simplify expressions involving higher-order roots?
5. What are some common mistakes when working with square roots?

**Tip:** When dealing with square roots, always try to simplify them by factoring the radicand into perfect squares!

Explore why √8 = √2 + √2 is both correct and how to simplify square root expressions. Learn about square root properties and algebraic operations involving square roots. Suitable for Grades 7-9.

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