https://file.aiquickdraw.com/mathbot/file/1726491359292y3mlrgdm.jpg

Let's go through the image step by step and solve the square roots that I see written:

1. **\(\sqrt{50} + \sqrt{8} + \sqrt{18}\):**
   - Break down each square root:
     - \(\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}\)
     - \(\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}\)
     - \(\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}\)
   - Combine terms: 
     - \(5\sqrt{2} + 2\sqrt{2} + 3\sqrt{2} = 10\sqrt{2}\)

2. **\(\sqrt{19} + \sqrt{192}\):**
   - Simplify the terms:
     - \(\sqrt{19}\) is already simplified.
     - \(\sqrt{192} = \sqrt{64 \times 3} = 8\sqrt{3}\)
   - The expression becomes: 
     - \(\sqrt{19} + 8\sqrt{3}\)

3. **\(\sqrt{10} + \sqrt{84}\):**
   - Simplify the square roots:
     - \(\sqrt{10}\) is already simplified.
     - \(\sqrt{84} = \sqrt{4 \times 21} = 2\sqrt{21}\)
   - The expression becomes:
     - \(\sqrt{10} + 2\sqrt{21}\)

Would you like more detailed explanations or further clarifications on these steps?

Here are some related questions to expand understanding:

1. How can you identify whether a square root can be simplified further?
2. What is the process for combining terms involving square roots?
3. How does the prime factorization of a number help in simplifying square roots?
4. What is the difference between simplifying square roots and combining them?
5. Can irrational numbers like \(\sqrt{2}\) ever be simplified into rational numbers?

**Tip:** Always check for perfect square factors inside square roots for simplification.

Solve the expressions involving square roots: \(\sqrt{50} + \sqrt{8} + \sqrt{18}\), \(\sqrt{19} + \sqrt{192}\), and \(\sqrt{10} + \sqrt{84}\).

Learn how to simplify expressions involving square roots such as \(\sqrt{50} + \sqrt{8} + \sqrt{18}\) and \(\sqrt{19} + \sqrt{192}\) with step-by-step breakdowns. This tutorial covers key concepts of simplifying square roots and combining radicals. Suitable for students in Grades 7-10.

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