https://file.aiquickdraw.com/mathbot/file/1729738968973wo26uciy.jpg

Let's simplify the given expression:

\[
3\sqrt{200} - \sqrt{32} + 8\sqrt{8}
\]

### Step 1: Simplify each square root
- \(\sqrt{200} = \sqrt{100 \times 2} = 10\sqrt{2}\)
- \(\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}\)
- \(\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}\)

### Step 2: Substitute these simplified values into the original expression
\[
3\sqrt{200} - \sqrt{32} + 8\sqrt{8} = 3(10\sqrt{2}) - 4\sqrt{2} + 8(2\sqrt{2})
\]
\[
= 30\sqrt{2} - 4\sqrt{2} + 16\sqrt{2}
\]

### Step 3: Combine like terms
All terms have \(\sqrt{2}\), so we can combine them:
\[
30\sqrt{2} - 4\sqrt{2} + 16\sqrt{2} = (30 - 4 + 16)\sqrt{2} = 42\sqrt{2}
\]

### Final Answer:
\[
42\sqrt{2}
\]

Let me know if you want more details or have any questions.

Here are 5 related questions to explore:
1. How do you simplify square roots with non-perfect squares?
2. Can you add and subtract square roots with different radicands?
3. How would the process differ if a cube root were involved instead of a square root?
4. What are the properties of radicals that allow combining like terms?
5. How do coefficients affect the simplification of radical expressions?

**Tip:** Always look for the largest perfect square factor when simplifying square roots, as this helps reduce the expression efficiently.

Simplify the expression 3√200 − √32 + 8√8 by collecting like radical terms.

Learn how to simplify the radical expression 3√200 − √32 + 8√8. This step-by-step solution involves breaking down the square roots and combining like radical terms, a concept crucial in algebra for students in Grades 9-11.

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