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The image contains a square root problem involving the square root of 200, as well as instructions asking for a list of all factors involved. Let's break down the problem step-by-step:

### Problem: Simplify \( \sqrt{200} \).

#### Step 1: Factorize 200
To simplify the square root, we need to find the factors of 200. Here is the prime factorization of 200:

\[
200 = 2^3 \times 5^2
\]

#### Step 2: Simplify the Square Root
Now, apply the square root to the factors of 200:

\[
\sqrt{200} = \sqrt{2^3 \times 5^2} = \sqrt{2^3} \times \sqrt{5^2}
\]

\[
\sqrt{200} = 2 \times 5 \times \sqrt{2} = 10\sqrt{2}
\]

Thus, the simplified form of \( \sqrt{200} \) is:

\[
\boxed{10\sqrt{2}}
\]

Would you like to discuss this in further detail or do you have any questions?

### Related Questions:
1. What are the factors of 200?
2. How do you simplify square roots of larger numbers?
3. What are prime factors, and how do they help in simplifying square roots?
4. How do you solve problems involving non-perfect square roots?
5. What is the difference between perfect squares and non-perfect squares?

### Tip:
When simplifying square roots, always break down the number into its prime factors to identify which factors can be taken out of the square root.

Simplify the square root of 200 and list its factors.

Learn how to simplify the square root of 200 using prime factorization. This step-by-step guide shows how to break down 200 into its prime factors and simplify the expression. Suitable for students in Grades 7-9.

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